//#define READ_NUM_TEST_CASES
//#define ASSERTS		// force asserts on online judge
//#define FASTIO

//#define DEBUG_BUILD

//#include<atablash/splay/common.hpp>
//#include<atablash/splay/node.hpp>

//#include<atablash/interval-tree.hpp>






#include<stdint.h>

#include<utility>

#include<vector>
#include<memory>




// abbrevs

typedef unsigned int uint;

typedef int8_t i8;
typedef uint8_t ui8;
typedef int16_t i16;
typedef uint16_t ui16;
typedef int32_t i32;
typedef uint32_t ui32;
typedef int64_t i64;
typedef uint64_t ui64;

// old:
typedef i64 ll;
typedef ui64 ull;

typedef std::pair<i32,i32> pii;
typedef std::pair<double,double> pdd;

typedef std::vector<i32> vi;
#define VE std::vector

#define umap std::unordered_map
#define umultimap std::unordered_multimap
#define uset std::unordered_set
#define umultiset std::unordered_multiset

typedef unsigned short ushort;
typedef unsigned char uchar;


template<class T> using sptr = std::shared_ptr<T>;
template<class T> using uptr = std::unique_ptr<T>;
template<class A, class B> using p = std::pair<A, B>;



namespace ab{

struct Void {};


// convert to float with enough precision
template<typename I>struct FloatFrom{typedef Void R;};
template<>struct FloatFrom<i32>{typedef double R;};
template<>struct FloatFrom<ui32>{typedef double R;};
template<>struct FloatFrom<i64>{typedef long double R;};
template<>struct FloatFrom<ui64>{typedef long double R;};
template<>struct FloatFrom<i16>{typedef float R;};
template<>struct FloatFrom<ui16>{typedef float R;};
template<>struct FloatFrom<i8>{typedef float R;};
template<>struct FloatFrom<ui8>{typedef float R;};
template<>struct FloatFrom<float>{typedef float R;};
template<>struct FloatFrom<double>{typedef double R;};
template<>struct FloatFrom<long double>{typedef long double R;};

// get type capable of storing multiplication result
template<typename I>struct Double{typedef Void R;};
template<>struct Double<i8>{typedef i16 R;};
template<>struct Double<ui8>{typedef ui16 R;};
template<>struct Double<i16>{typedef i32 R;};
template<>struct Double<ui16>{typedef ui32 R;};
template<>struct Double<i32>{typedef i64 R;};
template<>struct Double<ui32>{typedef ui64 R;};

template<>struct Double<float>{typedef float R;};
template<>struct Double<double>{typedef double R;};
template<>struct Double<long double>{typedef long double R;};



#if defined __GNUC__ && ( defined __x86_64__ || defined __ppc64__ || defined __MINGW64__ )
typedef __int128_t i128;
typedef __uint128_t ui128;
template<>struct Double<i64>{typedef i128 R;};
template<>struct Double<ui64>{typedef ui128 R;};
#endif


}


// enable debug if any debug macro is defined
#if (defined _DEBUG || defined DEBUG) && !defined DEBUG_BUILD
#define DEBUG_BUILD
#endif

// DEBUG_BUILD (set or not set) overrides NDEBUG
#ifdef DEBUG_BUILD
	#undef NDEBUG
	//#pragma message "Compiling in DEBUG mode."
#else
	#ifndef NDEBUG
	#define NDEBUG
	#endif
#endif

//#include <cstdio>
//#include <cfloat>




//#include<type_traits>


#define _CAT(a,b) a##b
#define CAT(a,b) _CAT(a,b)
#define _10TH(a,b,c,d,e,f,g,h,i,X,...) X
#define VA_CNT(...) _10TH(__VA_ARGS__,9,8,7,6,5,4,3,2,1,0)
#define VA_SEL(a,...) CAT(a,VA_CNT(__VA_ARGS__))(__VA_ARGS__)

#define _VA_GTONE(...) _10TH(__VA_ARGS__,1,1,1,1,1,1,1,1,0,0)
#define VA_GTONE(a,...) CAT(a,_VA_GTONE(__VA_ARGS__))(__VA_ARGS__)


#define MIN_GCC(a,b,c) (__GNUC__ > (a) || \
              (__GNUC__ == (a) && (__GNUC_MINOR__ > (b) || \
                                 (__GNUC_MINOR__ == (b) && \
								 __GNUC_PATCHLEVEL__ >= (c)))))





// TODO: po co to bylo??
/*
#include<functional>
#if __cplusplus >= 201103L
namespace std
{
    template<class T>
    struct hash
    {
        typedef T argument_type;
        typedef typename std::underlying_type< argument_type >::type underlying_type;
        typedef typename std::hash< underlying_type >::result_type result_type;
        result_type operator()( const argument_type& arg ) const
        {
            std::hash< underlying_type > hasher;
            return hasher( static_cast< underlying_type >( arg ) );
        }
    };
}
#endif
*/


#define bac back()
#define fro front()
#define emp empty()
#define fi first
#define se second
#define siz size()
#define ins insert
#define era erase
#define mp make_pair
#define be begin()
#define en end()
#define rbe rbegin()
#define ren rend()
#define pub push_back
#define puf push_front
#define pob pop_back()
#define pof pop_front()
#define bs binary_search
#define lb lower_bound
#define ub upper_bound
#define pq priority_queue
#define si (int)


#undef FO
#undef OF

#define FOR(i,n) for(int i=0; i<(int)(n); ++i)
#define FO(i,a,b) for(int i=(a); i<(int)(b); ++i)
#define OF(i,a,b) for(int i=(int)(b)-1;i>=(int)(a);--i)
#define FE(it,c)  for(__typeof((c).begin()) it=(c).begin(); it!=(c).end(); ++it)
#define FER(it,c) for(__typeof((c).begin()) it=(c).begin(); it!=(c).end(); )
#define ALL(c) (c).begin(),(c).end()
#define ZERO(c) memset(c,0,sizeof(c))

#define AU(v,val) __typeof(val) v(val)

const char NL='\n';
const char SP=' ';






// Visual C++ intristics
#ifdef _MSC_VER
	#include <intrin.h>
	#define __builtin_popcount __popcnt

	#ifdef _WIN64
		#define __builtin_popcountll __popcnt64
	#else
		inline int __builtin_popcountll(__int64 a){ return __builtin_popcount((ui32)a) + __builtin_popcount(a >> 32); }
	#endif 
#endif


// Visual C++ 'and', 'or', 'not'
#ifdef _MSC_VER
	#define and &&
	#define or ||
	#define not !
#endif


namespace ab{

template<class T>inline T cbitl(T x,int i){return (x<<i) ^ (x>>(sizeof(T)*8-i));} // cycle bits left
inline int popcount(uint i){return __builtin_popcount(i);}
inline int popcount(ull i){return __builtin_popcountll(i);}

#ifdef __GNUC__
inline int parity(uint i){return __builtin_parity(i);}
inline int parity(ull i){return __builtin_parityll(i);}
inline int ilog2(uint i){return 31-__builtin_clz(i);} // int log; floor(log2(i))
inline int ilog2(ull i){return 63-__builtin_clzll(i);}
#endif


template<class T>inline bool isPowerOf2(const T&x){return !(x&(x-1));}



struct Static{
	Static() = default;
	Static(const Static&) = delete;
	Static(Static&&) = delete;
	Static(const Static&&) = delete;
	Static& operator=(const Static&) = delete;
	Static& operator=(Static&&) = delete;
	Static& operator=(const Static&&) = delete;
};



}






#include<vector>
#include<unordered_map>


// ?
#include<iostream>
#include<fstream>
#include<string>
#include<algorithm>
#include<mutex>

// to_string fix for MinGW





#include<map>
#include<iostream>



#if __cplusplus >= 201103L or defined _MSC_VER
#include <unordered_map>
#include <unordered_set>
namespace std{
#else
#include <ext/hash_map>
#include <ext/hash_set>
namespace __gnu_cxx{
#define unordered_map hash_map
#define unordered_multimap hash_multimap
#define unordered_set hash_set
#define unordered_multiset hash_multiset
/*
template<class K, class V> class unordered_map : public hash_map<K,V>{
public:
	typename hash_map<K,V>::iterator erase(const typename hash_map<K,V>::iterator& it){
		typename hash_map<K,V>::iterator r = it;
		++r;
		if(r!=hash_map<K,V>::end()){
			K key = r->first;
			hash_map<K,V>::erase(it);
			return hash_map<K,V>::find(key);
		}
		else{
			hash_map<K,V>::erase(it);
			return r;
		}
	}
	typename hash_map<K,V>::size_type erase(const K& key){
		return hash_map<K,V>::erase(key);
	}
};
*/
#endif

// 1,2,last (!!!!!)
/*template<>*/ template<class A,class B>struct hash<std::map<A,B> >{
    size_t operator()(const std::map<A,B>& m) const{
        size_t r = m.size();
        if(!r)return 0;
        __typeof(m.begin()) i=m.be;
        r^=hash<__typeof(i)>()(i);
        ++i;
        r^=cbitl(hash<__typeof(i)>()(*i),sizeof(r)*8/4);
        i=m.end();
        --i;
        r^=cbitl(hash<__typeof(i)>()(*i),sizeof(r)*8/2);
        return r;
    }
};



// hash pairs:
/*template<>*/ template<class A, class B>struct hash<pair<A,B> >{
    size_t operator()(const pair<A,B>& p) const{
        return hash<A>()(p.first) ^ ab::cbitl(hash<B>()(p.second),sizeof(size_t)*8/2);
    }
};



// hash enums:
//
// TODO: fix for msvc
#if defined __GNUC__ and MIN_GCC(4,8,4)
template<class E> struct hash {
    using sfinae = typename std::enable_if<std::is_enum<E>::value, E>::type;
public:
    size_t operator()(const E&e) const {
      return std::hash<typename std::underlying_type<E>::type>()((typename std::underlying_type<E>::type)e);
    }
};
#endif
  
} // namespace std / __gnu_cxx








// component-wise pair operators
template<class A, class B, class C, class D>
inline std::pair<A,B>& operator+=(std::pair<A,B>& p, const std::pair<C,D>& o){
	p.first+=o.first;
	p.second+=o.second;
	return p;
}
template<class A, class B, class C, class D>
inline std::pair<A,B>& operator-=(std::pair<A,B>& p, const std::pair<C,D>& o){
	p.first-=o.first;
	p.second-=o.second;
	return p;
}
template<class A, class B, class C, class D>
inline std::pair<A,B>& operator*=(std::pair<A,B>& p, const std::pair<C,D>& o){
	p.first*=o.first;
	p.second*=o.second;
	return p;
}
template<class A, class B, class C, class D>
inline std::pair<A,B>& operator/=(std::pair<A,B>& p, const std::pair<C,D>& o){
	p.first/=o.first;
	p.second/=o.second;
	return p;
}

template<class Afi, class Ase, class Bfi, class Bse>
inline std::pair<decltype(Afi() + Bfi()), decltype(Ase() + Bse())>&
operator+(const std::pair<Afi,Ase>& a, const std::pair<Bfi,Bse>& b){
	return std::make_pair(a.fi+b.fi, a.se+b.se);
}
template<class Afi, class Ase, class Bfi, class Bse>
inline std::pair<decltype(Afi() - Bfi()), decltype(Ase() - Bse())>&
operator-(const std::pair<Afi,Ase>& a, const std::pair<Bfi,Bse>& b){
	return std::make_pair(a.fi-b.fi, a.se-b.se);
}
template<class Afi, class Ase, class Bfi, class Bse>
inline std::pair<decltype(Afi()*Bfi()), decltype(Ase()*Bse())>&
operator*(const std::pair<Afi,Ase>& a, const std::pair<Bfi,Bse>& b){
	return std::make_pair(a.fi*b.fi, a.se*b.se);
}
template<class Afi, class Ase, class Bfi, class Bse>
inline std::pair<decltype(Afi() / Bfi()), decltype(Ase() / Bse())>&
operator/(const std::pair<Afi,Ase>& a, const std::pair<Bfi,Bse>& b){
	return std::make_pair(a.fi/b.fi, a.se/b.se);
}








// vector operators
template<class T, class U>
inline std::vector<T>& operator+=(std::vector<T>& v, const std::vector<U>& o){
	ASS(v.siz == o.siz);
	FOR(i,v.siz) v[i] += o[i];
	return v;
}


template<class T>
inline std::vector<T>& operator*=(std::vector<T>& v, const T& a){
	FOR(i,v.siz) v[i] *= a;
	return v;
}





// serialization
template<class A,class B>inline std::ostream&operator<<(std::ostream&o,const std::pair<A,B>&p){o<<'<'<<p.first<<", "<<p.second<<'>';return o;}
template<class A,class B>inline std::ostream&operator<<(std::ostream&o,const std::map<A,B>&m){o<<'\n';FE(k,m)o<<"map["<<k->first<<"] -> "<<k->se<<'\n';return o;}
template<class A,class B>inline std::ostream&operator<<(std::ostream&o,const umap<A,B>&m){o<<'\n';FE(k,m)o<<"umap["<<k->first<<"] -> "<<k->se<<'\n';return o;}
template<class A,class B>inline std::ostream&operator<<(std::ostream&o,const uset<A,B>&_m){o<<"uset{\n";FE(k,_m)o<<*k<<'\n';o<<'\n';return o;}
template<class A>inline std::ostream&operator<<(std::ostream&o,const std::vector<A>&_v){o<<'\n';FOR(i,_v.siz)o<<"vector["<<i<<"] = "<<_v[i]<<"}\n";return o;}





// fix for MinGW: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=52015
#ifdef _GLIBCXX_HAVE_BROKEN_VSWPRINTF
namespace std{
	template<class T>
	inline string to_string(const T& t){
		stringstream ss;
		ss << t;
		return ss.str();
	}
}
#endif





//#define  LOG0(str) 			fprintf(stderr,"%s:%d - " str "\n",__FILE__,__LINE__)
//#define  LOG1(str,...)		fprintf(stderr,"%s:%d - " str "\n",__FILE__,__LINE__,__VA_ARGS__)
//#define LOG(...) VA_GTONE(LOG,__VA_ARGS__)


#define LOGD(str) if(ab::Log::global()) ab::Log::global()->debug(str,__FILE__,__LINE__)
#define LOGI(str) if(ab::Log::global()) ab::Log::global()->info(str,__FILE__,__LINE__)
#define LOGW(str) if(ab::Log::global()) ab::Log::global()->warning(str,__FILE__,__LINE__)
#define LOGE(str) if(ab::Log::global()) ab::Log::global()->error(str,__FILE__,__LINE__)
#define LOGF(str) if(ab::Log::global()) ab::Log::global()->fail(str,__FILE__,__LINE__)

	


namespace ab{


// TODO: czas logowania
// TODO: interfejs do dodawania nazw message levelom, ustawiania nazwy pliku z logiem, czy printowac na stderr, ...
//
// level >= DEBUG powoduje ignorowanie logowania w release
class Log{
public:
	enum{
		DEBUG = 5000,
		INFO = 4000, // default?
		WARNING = 3000,
		ERROR = 2000,
		FAIL = 1000};

public:
	void debug(const std::string& _message, const std::string& file="", int line=0){
		message(DEBUG, _message, file, line);
	}
	void info(const std::string& _message, const std::string& file = "", int line = 0){
		message(INFO, _message, file, line);
	}
	void warning(const std::string& _message, const std::string& file = "", int line = 0){
		message(WARNING, _message, file, line);
	}
	void error(const std::string& _message, const std::string& file = "", int line = 0){
		message(ERROR, _message, file, line);
	}
	void fail(const std::string& _message, const std::string& file = "", int line = 0){
		message(FAIL, _message, file, line);
	}

	// slow
	void flushConsole(){
		// avoid slow cout during lock
		// copy messages to print
		static const uint max_messages_flush = 128;
		std::vector<Message> messages_copy;
		{
			std::lock_guard<std::mutex> lock(mut);
			messages_copy.assign(messages.begin() + numPrinted, messages.begin() + numPrinted + std::min(max_messages_flush, (uint)messages.size() - numPrinted));
		}

		for (uint i = 0; i < messages_copy.size(); ++i){
			std::cout << messageToString(messages_copy[i]) << '\n';
		}
		std::cout.flush();

		numPrinted += messages_copy.size();
	}

	void message(int level, const std::string& messageText, const std::string& file = "", int line = 0){

		#if !defined DEBUG_BUILD
			if (level >= DEBUG) return;
		#endif
		
		std::lock_guard<std::mutex> lock(mut);

		messages.push_back(Message{ level, messageText, file, line });
		
		//if(autoFlush) flushConsole();

		#ifdef DEBUG_BUILD
			if (level <= ERROR){
				#ifdef _MSC_VER
					__debugbreak();
				#endif
				#ifdef __GNUC__
					__builtin_trap();
				#endif
			}
		#endif

	}


	// reference to pointer. client should create the log himself
	static Log*& global(){
		static Log* log = nullptr;
		return log;
	}

public:
	Log(){
		levelNames[DEBUG] = "DEBUG";
		levelNames[INFO] = "INFO";
		levelNames[WARNING] = "WARNING";
		levelNames[ERROR] = "ERROR";
		levelNames[FAIL] = "FAIL";
	}
	~Log(){
		if (filename != ""){
			std::ofstream os(filename);
			for (auto&m : messages){
				os << messageToString(m) << '\n';
			}
		}
	}
	
	//bool autoFlush = false;

private:
	struct Message{
		int level;
		std::string text;
		std::string file;
		int line;
	};
	
	static std::string shortenPath(const std::string& s){
		std::string result = s;
		std::string ss[] = {"include/", "include\\", "src/", "src\\"};
		for(uint i=0; i<sizeof(ss)/sizeof(std::string); ++i){
			auto pos = result.rfind(ss[i]);
			if(pos == std::string::npos) continue;
			
			result = result.substr(pos + ss[i].size(), std::string::npos);
		}
		return result;
	}

	std::string messageToString(const Message& m) const {
		std::string levelName;
		auto r = levelNames.find(m.level);
		if (r == levelNames.end()) levelName = std::to_string(m.level);
		else levelName = r->second;
		std::string result = levelName + ": " + m.text;
		if (m.file != "") result += " at " + shortenPath(m.file) + ":" + std::to_string(m.line);
		return result;
	}

	uint numPrinted = 0;
	std::vector<Message> messages;
	std::mutex mut; // TODO: spinlock

	std::unordered_map<int, std::string> levelNames;
	std::string filename = "atablash.log";

private:
	Log(const Log&) = delete;
	Log& operator=(const Log&) = delete;
};










}





inline void breakpoint(){}
#ifdef NDEBUG
	#define DE if(0)
#else // DEBUG
	#define DE
#endif


#if defined NDEBUG && not defined ASSERTS
	#define ASS(x)
	#define FLOAT_OK(x)
	#define ASSERT_FLOAT(x)
#else
	#include<cassert>
	#define ASS(x) assert(x)
	#define FLOAT_OK(x) ((x) <= LDBL_MAX && (x) >= -LDBL_MAX)
	#define ASSERT_FLOAT(f) ASS(FLOAT_OK(f))
#endif

#define DV(x) (E<#x<": "<(x)<N)
#define XX E<"XX at line "<__LINE__<NL;


#if defined DEBUG_BUILD or defined COLOR_CONSOLE
	#ifdef _WIN32
	
		#ifndef NOMINMAX
		#define NOMINMAX
		#endif
		
		#ifndef WIN32_LEAN_AND_MEAN
		#define WIN32_LEAN_AND_MEAN
		#endif
		
		#include<windows.h>
		inline void ec(int a){static HANDLE h=GetStdHandle(-12);SetConsoleTextAttribute(h,a?12:0xf);}	// color 12
		inline void oc(int a){static HANDLE h=GetStdHandle(-11);SetConsoleTextAttribute(h,a?10:0xf);}	// color 10
	#else
		// *nix includes for debug
	#endif
#else
	#define ec(x)
	#define oc(x)
#endif



#include <iostream>
struct _E{template<class T>_E&operator<(const T&_t){DE{ec(1);std::cerr<<_t;ec(0);}return*this;}};





#ifdef __GNUC__
	#pragma GCC diagnostic push
	#pragma GCC diagnostic ignored "-Wunused-variable"	// not working
#endif

static _E E;

#ifdef __GNUC__
	#pragma GCC diagnostic pop
#endif




// E unused
#ifdef __GNUC__
	template<class T>void ___fhsdhsdhrtsh(){(void)E;}
#endif




#include<cstdlib>






namespace ab
{

	/*
	template<typename Ret, typename T>
	class Binder
	{
	public:
		Binder(Ret T::*_var) : var(_var) {}
		Ret& operator()(T& obj) const
		{
			return obj.*var;
		}
		const Ret& operator()(const T& obj) const
		{
			return obj.*var;
		}
	private:
		Ret T::*var;
	};

	template<typename Ret, typename T>
	Binder<Ret,T> bind(Ret T::*var)
	{
		return Binder<Ret,T>(var);
	}*/
	
	
	
	
	
	/*
	
	template<class A, class B>
	__typeof(A()+B()) plus(const A& a, const B& b){return a+b;}
	
	template<class A, class B>
	__typeof(A()-B()) minus(const A& a, const B& b){return a-b;}
	
	template<class A, class B>
	__typeof(A()*B()) multiplies(const A& a, const B& b){return a*b;}
	
	template<class A, class B>
	__typeof(A()/B()) divides(const A& a, const B& b){return a/b;}
	
	
	
	template<class A, class B>
	A& plus_assign(A& a,const B& b){return a+=b;}
	
	template<class A, class B>
	A& minus_assign(A& a,const B& b){return a-=b;}
	
	template<class A, class B>
	A& multiplies_assign(A& a,const B& b){return a*=b;}
	
	template<class A, class B>
	A& divides_assign(A& a,const B& b){return a/=b;}
	
	*/
	

}






//#include<type_traits>

namespace ab
{


template<bool cond, typename T, typename F> struct IF {typedef T R;};
template<typename T, typename F> struct IF<false,T,F> {typedef F R;};

template <bool B, class T = void> struct ENABLE_IF {typedef T R;};
template <class T> struct ENABLE_IF<false, T> {};

template <bool B, class T = void> struct DISABLE_IF {typedef T R;};
template <class T> struct DISABLE_IF<true, T> {};



template<class A, class B> struct SAME{ static const bool r = false;};
template<typename T> struct SAME<T,T>{	static const bool r = true;};


template<typename T>
struct IS_CLASS{
	template<typename C> static char (&f(int C::*))[1];
	template<typename C> static char (&f(...))[2];

	static bool const r = sizeof(f<T>(0))==sizeof(char);
};




// remove reference
template<class T> struct RR{typedef T R;};
template<class T> struct RR<T&>{typedef T R;};

//remove const
template<class T> struct RC{typedef T R;};
template<class T> struct RC<const T>{typedef T R;};

// remove const and reference
template<class T> struct RRC{typedef typename RC<typename RR<T>::R>::R R;};


#define TYPE(T,...) typename T<__VA_ARGS__>::R





struct TRU{static const bool r = true;  typedef TRU R;};
struct FAL{static const bool r = false; typedef FAL R;};



// SFINAE test
#define HAS_MEMBER(member_alias, member)																									\
template<typename __T> struct HAS_CLASS_##member_alias {																											\
    struct Fallback { void member(); };																											\
    struct Derived : __T, Fallback { };																											\
																											\
    template<typename C, C> struct ChT;																											\
																											\
    template<typename C> static char (&f(ChT<void (Fallback::*)(), &C::member>*))[1];													\
    template<typename C> static char (&f(...))[2];																								\
																											\
    static const bool r = sizeof(f<Derived>(0)) == 2;																						\
};																										\
template<typename __T>																											\
struct HAS_##member_alias																											\
{																											\
	typedef typename IF<IS_CLASS<__T>::r, HAS_CLASS_##member_alias<__T>, FAL>::R R;														\
	static const bool r = R::r;																									\
};






// Dzia│a dok│adnie, uwzglŕdnia typ (const, referencje) wyniku i argumentˇw, uwzglŕdnia const membera
// Przyk│ad dla non-static klasy A:
// typedef int (A::*sign1)(unsigned short&); 
// Przyk│ad dla static dowolnej klasy:
// typedef int (*sign1)(unsigned short&); 
#define HAS_MEMBER_SIG(member_name, member_signature)																			\
template<typename CLS>																							\
struct HAS_SIG_##member_name																															\
{																									\
    template<typename C, C> struct ChT;																													\
	template<typename C> static char (&f(ChT<member_signature, &C::member_name>*))[1];																\
	template<typename C> static char (&f(...))[2];																									\
	static const bool r = sizeof(f<CLS>(0)) == sizeof(char);																							\
};




HAS_MEMBER(OPERATOR_CALL, operator())




/*
// get &T::x or &T::first
template<class T,class=void>struct GET_X{};
template<class T>struct GET_X<T,typename std::enable_if<std::is_object<decltype(T::x)>::value>::type>{typedef decltype(&T::x) R;};
template<class T>struct GET_X<T,typename std::enable_if<std::is_object<decltype(T::first)>::value>::type>{typedef decltype(&T::first) R;};

// get &T::y or &T::second
template<class T,class=void>struct GET_Y{};
template<class T>struct GET_Y<T,typename std::enable_if<std::is_object<decltype(T::y)>::value>::type>{typedef decltype(&T::y) R;};
template<class T>struct GET_Y<T,typename std::enable_if<std::is_object<decltype(T::second)>::value>::type>{typedef decltype(&T::second) R;};
*/

}






#include<utility>

namespace ab{

	struct Identity{
		template<class TT>
		TT operator()(TT&& x)const {
			return std::forward<TT>(x);
		}
		template<class TT>
		TT operator[](TT&& x) const {
			return std::forward<TT>(x);
		}
	};

}




namespace ab{

struct Lambda1{
	template<class A1>
	const A1& operator()(const A1& a1)const{return a1;}
	template<class A1>
	      A1& operator()(      A1& a1)const{return a1;}
	
	template<class A1,class A2>
	const A1& operator()(const A1& a1, const A2&)const{return a1;}
	template<class A1,class A2>
	      A1& operator()(      A1& a1, const A2&)const{return a1;}
	
	template<class A1,class A2,class A3>
	const A1& operator()(const A1& a1, const A2&, const A3&)const{return a1;}
	template<class A1,class A2,class A3>
	      A1& operator()(      A1& a1, const A2&, const A3&)const{return a1;}
};


struct Lambda2{
	template<class A1,class A2>
	const A2& operator()(const A1& a1, const A2& a2)const{return a2;}
	template<class A1,class A2>
	      A2& operator()(const A1& a1,       A2& a2)const{return a2;}
	
	template<class A1,class A2,class A3>
	const A2& operator()(const A1& a1, const A2& a2, const A3& a3)const{return a2;}
	template<class A1,class A2,class A3>
	      A2& operator()(const A1& a1,       A2& a2, const A3& a3)const{return a2;}
};


struct Lambda3{
	template<class A1,class A2,class A3>
	const A3& operator()(const A1& a1, const A2& a2, const A3& a3)const{return a3;}
	template<class A1,class A2,class A3>
	      A3& operator()(const A1& a1, const A2& a2,       A3& a3)const{return a3;}
};


#ifdef __GNUC__
	#pragma GCC diagnostic push
	#pragma GCC diagnostic ignored "-Wunused-variable"	// not working
#endif


static Lambda1 _1;
static Lambda2 _2;
static Lambda3 _3;
//#define _1 Lambda1()
//#define _2 Lambda2()
//#define _3 Lambda3()



#ifdef __GNUC__
#pragma GCC diagnostic pop
#endif




#ifdef __GNUC__
	// _1 _2 _3 unused
	// pragma diagnostic ignored not working?
	template<class T>void ___fhsdhsdhrtshx(){(void)_1;(void)_2;(void)_3;}
#endif







template<class L, class A1, class A2, class A3> struct RET_TYPE3{typedef L& R;};

template<class L, class A1> struct RET_TYPE1{typedef typename RET_TYPE3<L,A1,A1,A1>::R R;};
template<class L, class A1, class A2> struct RET_TYPE2{typedef typename RET_TYPE3<L,A1,A2,A2>::R R;};






// is lambda before evaluation
template<class L> struct IS_LAMBDA{static const bool r = false;};





// is lambda after evaluation
template<class L, class A1, class A2, class A3> struct IS_LAMBDA3{
static const bool r = !SAME<L&, typename RET_TYPE3<L,A1,A2,A3>::R&>::r;};

template<class L, class A1, class A2> struct IS_LAMBDA2{
static const bool r = !SAME<typename RR<L>::R, typename RR<typename RET_TYPE2<L,A1,A2>::R>::R>::r;};

template<class L, class A1> struct IS_LAMBDA1{
static const bool r = !SAME<typename RR<L>::R, typename RR<typename RET_TYPE1<L,A1>::R>::R>::r;};




template<class T, class A1>
typename ENABLE_IF  < IS_LAMBDA1<T,A1>::r,      typename RET_TYPE1<T,const A1>::R>::R Eval(const T& t, const A1& a1){return t(a1);}
template<class T, class A1>
typename ENABLE_IF  < IS_LAMBDA1<T,A1>::r,      typename RET_TYPE1<T,      A1>::R>::R Eval(const T& t,       A1& a1){return t(a1);}

template<class T, class A1>
typename DISABLE_IF < IS_LAMBDA1<T,A1>::r,      typename RET_TYPE1<T,A1>::R&>::R Eval(      T& t, const A1& a1){return t;}




template<class T, class A1, class A2>
typename ENABLE_IF < IS_LAMBDA2<T,A1,A2>::r,      typename RET_TYPE2<T,const A1,const A2>::R>::R Eval(const T& t, const A1& a1, const A2& a2){return t(a1,a2);}
template<class T, class A1, class A2>
typename ENABLE_IF < IS_LAMBDA2<T,A1,A2>::r,      typename RET_TYPE2<T,const A1,      A2>::R>::R Eval(const T& t, const A1& a1,       A2& a2){return t(a1,a2);}
template<class T, class A1, class A2>
typename ENABLE_IF < IS_LAMBDA2<T,A1,A2>::r,      typename RET_TYPE2<T,      A1,const A2>::R>::R Eval(const T& t,       A1& a1, const A2& a2){return t(a1,a2);}
template<class T, class A1, class A2>
typename ENABLE_IF < IS_LAMBDA2<T,A1,A2>::r,      typename RET_TYPE2<T,      A1,      A2>::R>::R Eval(const T& t,       A1& a1,       A2& a2){return t(a1,a2);}

template<class T, class A1, class A2>
typename DISABLE_IF< IS_LAMBDA2<T,A1,A2>::r,      typename RET_TYPE2<T,A1,A2>::R&>::R Eval(      T& t, const A1& a1, const A2& a2){return t;}




template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,const A1,const A2,const A3>::R>::R Eval(const T& t, const A1& a1, const A2& a2, const A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,const A1,const A2,      A3>::R>::R Eval(const T& t, const A1& a1, const A2& a2,       A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,const A1,      A2,const A3>::R>::R Eval(const T& t, const A1& a1,       A2& a2, const A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,const A1,      A2,      A3>::R>::R Eval(const T& t, const A1& a1,       A2& a2,       A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,      A1,const A2,const A3>::R>::R Eval(const T& t,       A1& a1, const A2& a2, const A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,      A1,const A2,      A3>::R>::R Eval(const T& t,       A1& a1, const A2& a2,       A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,      A1,      A2,const A3>::R>::R Eval(const T& t,       A1& a1,       A2& a2, const A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,      A1,      A2,      A3>::R>::R Eval(const T& t,       A1& a1,       A2& a2,       A3& a3){return t(a1,a2,a3);}

template<class T, class A1, class A2, class A3>
typename DISABLE_IF < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,A1,A2,A3>::R&>::R Eval(      T& t, const A1& a1, const A2& a2, const A3& a3){return t;}







template<class L1, class L2>
class LambdaPlus{
public:
	LambdaPlus(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaPlus,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) + Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaPlus,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) + Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaPlus,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) + Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};

template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaPlus<L1,L2> >::R operator+(const L1& l1, const L2& l2){
	return LambdaPlus<L1,L2>(l1,l2);
}



template<class L1, class L2>
class LambdaMinus{
public:
	LambdaMinus(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaMinus,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) - Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaMinus,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) - Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaMinus,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) - Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};

template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaMinus<L1,L2> >::R operator-(const L1& l1, const L2& l2){
	return LambdaMinus<L1,L2>(l1,l2);
}






template<class L1>
class LambdaUnaryMinus{
public:
	LambdaUnaryMinus(const L1& _l1) : l1(_l1){}
	
	template<class A1>
	typename RET_TYPE1<LambdaUnaryMinus,A1>::R operator()(const A1& a1)const{
		return -Eval(l1,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaUnaryMinus,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return -Eval(l1,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaUnaryMinus,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return -Eval(l1,a1,a2,a3);
	}
	
private:
	const L1& l1;
};

template<class L1>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r, LambdaUnaryMinus<L1> >::R operator-(const L1& l1){
	return LambdaUnaryMinus<L1>(l1);
}






template<class L1, class L2>
class LambdaMultiplies{
public:
	LambdaMultiplies(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaMultiplies,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) * Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaMultiplies,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) * Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaMultiplies,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) * Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};

template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaMultiplies<L1,L2> >::R operator*(const L1& l1, const L2& l2){
	return LambdaMultiplies<L1,L2>(l1,l2);
}




template<class L1, class L2>
class LambdaDivides{
public:
	LambdaDivides(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaDivides,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) / Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaDivides,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) / Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaDivides,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) / Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};

template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaDivides<L1,L2> >::R operator/(const L1& l1, const L2& l2){
	return LambdaDivides<L1,L2>(l1,l2);
}














template<class L1, class L2>
class LambdaPlusAssign{
public:
	LambdaPlusAssign(L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1> typename RET_TYPE1<LambdaPlusAssign,A1>::R operator()(const A1& a1)const{return Eval(l1,a1) += Eval(l2,a1);}
	template<class A1> typename RET_TYPE1<LambdaPlusAssign,A1>::R operator()(      A1& a1)const{return Eval(l1,a1) += Eval(l2,a1);}
	
	template<class A1, class A2> typename RET_TYPE2<LambdaPlusAssign,const A1,const A2>::R operator()(const A1& a1, const A2& a2)const{return Eval(l1,a1,a2) += Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaPlusAssign,const A1,      A2>::R operator()(const A1& a1,       A2& a2)const{return Eval(l1,a1,a2) += Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaPlusAssign,      A1,const A2>::R operator()(      A1& a1, const A2& a2)const{return Eval(l1,a1,a2) += Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaPlusAssign,      A1,      A2>::R operator()(      A1& a1,       A2& a2)const{return Eval(l1,a1,a2) += Eval(l2,a1,a2);}
	
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(const A1& a1, const A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(const A1& a1,       A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(const A1& a1,       A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(      A1& a1, const A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(      A1& a1, const A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(      A1& a1,       A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(      A1& a1,       A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	
private:
	L1& l1;
	const L2& l2;
};


template<class L1, class L2>
typename ENABLE_IF<IS_LAMBDA<L1>::r or IS_LAMBDA<L2>::r, LambdaPlusAssign<L1,L2> >::R operator+=(L1& l1, const L2& l2){
	return LambdaPlusAssign<L1,L2>(l1,l2);
}







// LOGICAL

template<class L1, class L2>
class LambdaLess{
public:
	LambdaLess(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaLess,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) < Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaLess,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) < Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaLess,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) < Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};
template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaLess<L1,L2> >::R operator<(const L1& l1, const L2& l2){
	return LambdaLess<L1,L2>(l1,l2);
}





template<class L1, class L2>
class LambdaGreater{
public:
	LambdaGreater(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaGreater,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) > Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaGreater,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) > Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaGreater,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) > Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};

template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaGreater<L1,L2> >::R operator>(const L1& l1, const L2& l2){
	return LambdaGreater<L1,L2>(l1,l2);
}






template<class L1, class L2>
class LambdaDotStar{
public:
	LambdaDotStar(L1& _l1, const L2& _l2) : l1(_l1), l2(_l2) {}
	
	template<class A1> typename RET_TYPE1<LambdaDotStar,const A1>::R operator()(const A1& a1)const{return Eval(l1,a1).*Eval(l2,a1);}
	template<class A1> typename RET_TYPE1<LambdaDotStar,      A1>::R operator()(      A1& a1)const{return Eval(l1,a1).*Eval(l2,a1);}
	
	template<class A1, class A2> typename RET_TYPE2<LambdaDotStar,const A1,const A2>::R operator()(const A1& a1, const A2& a2)const{return Eval(l1,a1,a2).*Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaDotStar,const A1,      A2>::R operator()(const A1& a1,       A2& a2)const{return Eval(l1,a1,a2).*Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaDotStar,      A1,const A2>::R operator()(      A1& a1, const A2& a2)const{return Eval(l1,a1,a2).*Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaDotStar,      A1,      A2>::R operator()(      A1& a1,       A2& a2)const{return Eval(l1,a1,a2).*Eval(l2,a1,a2);}
	
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,const A1,const A2,const A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,const A1,const A2,      A3>::R operator()(const A1& a1, const A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,const A1,      A2,const A3>::R operator()(const A1& a1,       A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,const A1,      A2,      A3>::R operator()(const A1& a1,       A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,      A1,const A2,const A3>::R operator()(      A1& a1, const A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,      A1,const A2,      A3>::R operator()(      A1& a1, const A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,      A1,      A2,const A3>::R operator()(      A1& a1,       A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,      A1,      A2,      A3>::R operator()(      A1& a1,       A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}

private:
	L1& l1;
	const L2& l2;
};

// bv == bind var
template<class PTR, class T>
LambdaDotStar<const T,PTR> bv(const PTR& ptr, const T& t){
	return LambdaDotStar<const T,PTR>(t,ptr);
}
template<class PTR, class T>
LambdaDotStar<T,PTR> bv(const PTR& ptr, T& t){
	return LambdaDotStar<T,PTR>(t,ptr);
}








// is lambda (before evaluation)
template<> struct IS_LAMBDA<Lambda1>{static const bool r = true;};
template<> struct IS_LAMBDA<Lambda2>{static const bool r = true;};
template<> struct IS_LAMBDA<Lambda3>{static const bool r = true;};
template<class A,class B> struct IS_LAMBDA<LambdaPlus<A,B> >{static const bool r = true;};
template<class A,class B> struct IS_LAMBDA<LambdaMinus<A,B> >{static const bool r = true;};
template<class A,class B> struct IS_LAMBDA<LambdaMultiplies<A,B> >{static const bool r = true;};
template<class A,class B> struct IS_LAMBDA<LambdaDivides<A,B> >{static const bool r = true;};
template<class A,class B> struct IS_LAMBDA<LambdaPlusAssign<A,B> >{static const bool r = true;};
// TODO
















// lambda return types

/*
template<class A1> struct RET_TYPE1<Lambda1,A1>{typedef A1 R;};

template<class A1, class A2> struct RET_TYPE2<Lambda1,A1,A2>{typedef A1 R;};
template<class A1, class A2> struct RET_TYPE2<Lambda2,A1,A2>{typedef A2 R;};
*/
template<class A1, class A2, class A3> struct RET_TYPE3<Lambda1,A1,A2,A3>{typedef A1& R;};
template<class A1, class A2, class A3> struct RET_TYPE3<Lambda2,A1,A2,A3>{typedef A2& R;};
template<class A1, class A2, class A3> struct RET_TYPE3<Lambda3,A1,A2,A3>{typedef A3& R;};




#ifdef _MSC_VER
	#define __typeof decltype
#endif



template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaPlus<L1,L2>,A1,A2,A3>{
	typedef __typeof(TYPE(RRC,typename RET_TYPE3<L1,A1,A2,A3>::R)() + TYPE(RRC,typename RET_TYPE3<L2,A1,A2,A3>::R)()) R;
};

template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaMinus<L1,L2>,A1,A2,A3>{
	typedef __typeof(TYPE(RRC,typename RET_TYPE3<L1,A1,A2,A3>::R)() - TYPE(RRC,typename RET_TYPE3<L2,A1,A2,A3>::R)()) R;
};

template<class L1, class A1, class A2, class A3> struct RET_TYPE3<LambdaUnaryMinus<L1>,A1,A2,A3>{
	typedef __typeof(- TYPE(RRC,typename RET_TYPE3<L1,A1,A2,A3>::R)()) R;
};

template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaMultiplies<L1,L2>,A1,A2,A3>{
	typedef __typeof(*(typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R*)nullptr * *(typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R*)nullptr) R;
};

template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaDivides<L1,L2>,A1,A2,A3>{
	typedef __typeof(typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R() / typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R()) R;
};



template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaPlusAssign<L1,L2>,A1,A2,A3>{
	typedef __typeof(*(new typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R) += *(new typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R))& R;
};




template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaLess<L1,L2>,A1,A2,A3>{
	typedef __typeof(*(new typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R) < *(new typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R)) R;
};
template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaGreater<L1,L2>,A1,A2,A3>{
	typedef __typeof(*(new typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R) > *(new typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R)) R;
};



template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaDotStar<L1,L2>,A1,A2,A3>{
	typedef __typeof(*(new typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R) .* *(new typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R)) R;
};






template<class F, class L1>
class LambdaBinder1{
public:
	LambdaBinder1(const F& _f, const L1& _l1) : f(_f), l1(_l1) {}
	
	template<class A1>
	int operator()(const A1& a1){
		return f(Eval(l1,a1));
	}
	template<class A1, class A2>
	int operator()(const A1& a1, const A2& a2){
		return f(Eval(l1,a1,a2));
	}
	template<class A1, class A2, class A3>
	int operator()(const A1& a1, const A2& a2, const A3& a3){
		return f(Eval(l1,a1,a2,a3));
	}
	
private:
	const F& f;
	const L1& l1;
};

template<typename F, class L1>
LambdaBinder1<F,L1> bf(const F& f, const L1& l1){
	return LambdaBinder1<F,L1>(f,l1);
}



template<class F, class L1, class L2>
class LambdaBinder2{
public:
	LambdaBinder2(const F& _f, const L1& _l1, const L2& _l2) : f(_f), l1(_l1), l2(_l2) {}
	
	template<class A1>
	int operator()(const A1& a1){
		return f(Eval(l1,a1),Eval(l2,a1));
	}
	template<class A1, class A2>
	int operator()(const A1& a1, const A2& a2){
		return f(Eval(l1,a1,a2),Eval(l2,a1,a2));
	}
	template<class A1, class A2, class A3>
	int operator()(const A1& a1, const A2& a2, const A3& a3){
		return f(Eval(l1,a1,a2,a3),Eval(l2,a1,a2,a3));
	}
	
private:
	const F& f;
	const L1& l1;
	const L2& l2;
};

template<typename F, class L1, class L2>
LambdaBinder2<F,L1,L2> bf(const F& f, const L1& l1, const L2& l2){
	return LambdaBinder2<F,L1,L2>(f,l1,l2);
}



template<class F, class L1, class L2, class L3>
class LambdaBinder3{
public:
	LambdaBinder3(const F& _f, const L1& _l1, const L2& _l2, const L3& _l3) : f(_f), l1(_l1), l2(_l2), l3(_l3) {}
	
	template<class A1>
	int operator()(const A1& a1){
		return f(Eval(l1,a1),Eval(l2,a1),Eval(l3,a1));
	}
	template<class A1, class A2>
	int operator()(const A1& a1, const A2& a2){
		return f(Eval(l1,a1,a2),Eval(l2,a1,a2),Eval(l3,a1,a2));
	}
	template<class A1, class A2, class A3>
	int operator()(const A1& a1, const A2& a2, const A3& a3){
		return f(Eval(l1,a1,a2,a3),Eval(l2,a1,a2,a3),Eval(l3,a1,a2,a3));
	}
	
private:
	const F& f;
	const L1& l1;
	const L2& l2;
	const L3& l3;
};

template<typename F, class L1, class L2, class L3>
LambdaBinder3<F,L1,L2,L3> bf(const F& f, const L1& l1, const L2& l2, const L3& l3){
	return LambdaBinder3<F,L1,L2,L3>(f,l1,l2,l3);
}












}




namespace ab
{


// type-less!
#define PI 3.141592653589793238462643383279502884197169399375105820974944


template<typename T, typename IDX=int>
struct binomial
{
	binomial() : n(0), k(0), val(1) {}
	binomial(const IDX& nn, const IDX& kk) : n(nn), val(1){
		ASS(0<=kk);
		if(2*kk<nn){
			k = 0;
			while(k<kk)moveR();
		}
		else{
			k=nn;
			while(k>kk)moveL();
		}
	}
	IDX n,k;
	T val;
	
	operator T(){
		return val;
	}

	bool outside(){
		bool ret = n<0 || k<0 || k>n;
		if(ret)val=0;
		return ret;
	}

	void moveL(){
		--k;
		if(outside()) return;

		if(k==n) val=1;
		else
		{
			val*=(k+1);
			val/=(n-k);
		}
	}
	void moveR(){
		++k;
		if(outside()) return;

		if(k==0) val=1;
		else
		{
			val*=(n-k+1);
			val/=(k);
		}
	}
	void moveD(){
		++n;
		if(outside()) return;

		if(n==k) val=1;
		else
		{
			val*=n;
			val/=(n-k);
		}
	}
	void moveU(){
		--n;
		if(outside()) return;

		val*=(n-k+1);
		val/=(n+1);
	}
};



// GCD
#define gcd __gcd
/*
template<typename T>
T gcd(T a, T b)
{
	while(b!=0)
	{
		T t = a;
		a = a%b;
		b = t;
	}
	return a;
}
*/


// a*aa + b*bb == gcd(a,b)
template<typename T>
T gcdExt(T a, T b, T& aaa, T& bbb)
{
	T a0 = a;
	T b0 = b;

	T aa = 0;
	T bb = 1;
	aaa = 1;
	bbb = 0;
	// niezmiennik: a0*aa  + b0*bb  == b
	// niezmiennik: a0*aaa + b0*bbb == a
	while(b != 0)
	{
		T q = a/b;
		a = a%b;
		// a -= b*(a/b)
		aaa -= aa*q;
		bbb -= bb*q;
		swap(a,b);
		swap(aa,aaa);
		swap(bb,bbb);
	}

	ASS(a0*aaa + b0*bbb == a);

	return a;
}



template<class T, class E, class OP>
inline T fpow(T a, E exp, const OP& op, const T& neutral = 1){
	T r = neutral;
	while(exp){
		if(exp&1){
			r = op(r,a);
			--exp;
		}
		else{
			exp >>= 1;
			a = op(a,a);
		}
	}
	return r;
}

template<class T, class E>
inline T fpow(T a, E exp){
	return fpow(a, exp, _1 * _2);
}



template<class T> const T& max2(const T& a, const T& b){return a<b?b:a;}
template<class T> const T& min2(const T& a, const T& b){return b<a?b:a;}




template<class T, class F>
inline T lerp(const T& a, const T& b, const F& alpha){
	return (1.0f-alpha)*a + alpha*b;
}





}



namespace ab{

template<int mod1 = (1u<<31)-1, int mod2 = (1u<<31)-19>
struct H2{
	H2() : h1(0), h2(0) {}
	H2(int x) : h1(x%mod1), h2(x%mod2) {}
	ui32 h1,h2;
	H2& operator+=(const H2& o){
		h1 = (h1+o.h1)%mod1;
		h2 = (h2+o.h2)%mod2;
		return *this;
	}
	H2 operator+(const H2& o)const{
		return H2(*this)+=o;
	}
	H2& operator-=(const H2& o){
		h1 = (mod1+h1-o.h1)%mod1;
		h2 = (mod2+h2-o.h2)%mod2;
		return *this;
	}
	H2 operator-(const H2& o)const{
		return H2(*this)-=o;
	}
	H2& operator*=(const H2& o){
		h1 = (1ULL*h1*o.h1)%mod1;
		h2 = (1ULL*h2*o.h2)%mod2;
		return *this;
	}
	H2 operator*(const H2& o)const{
		return H2(*this)*=o;
	}

	bool operator==(const H2& o)const{
		return h1==o.h1 and h2==o.h2;
	}

	bool operator!=(const H2& o)const{
		return !operator==(o);
	}
};

template<int mod1 = (1u<<31)-1>
struct H1{
	H1() : h1(0) {}
	H1(int x) : h1(x%mod1) {}
	ui32 h1;
	H1& operator+=(const H1& o){
		h1 = (h1+o.h1);
		if(h1>=mod1)h1-=mod1;
		return *this;
	}
	H1 operator+(const H1& o)const{
		return H1(*this)+=o;
	}
	H1& operator-=(const H1& o){
		h1 = (mod1+h1-o.h1);
		if(h1>=mod1)h1-=mod1;
		return *this;
	}
	H1 operator-(const H1& o)const{
		return H1(*this)-=o;
	}
	H1& operator*=(const H1& o){
		h1 = (1ULL*h1*o.h1)%mod1;
		return *this;
	}
	H1 operator*(const H1& o)const{
		return H1(*this)*=o;
	}
	H1& operator/=(const H1& o){
		//ASS(millerRabin(mod1));
		return (*this)*=fpow(o, mod1-2, _1 * _2, H1(1));
	}
	H1 operator/(const H1& o)const{
		return H1(*this)/=o;
	}

	/*
	bool operator==(const H1& o)const{
		return h1==o.h1;
	}

	bool operator!=(const H1& o)const{
		return !operator==(o);
	}*/

	operator ui32()const{
		return h1;
	}
};





// hash long long,
// fpow multiplication
template<ull mod = (1ULL<<63)-25> // big prime less than (2^64)/2
struct HLL{
	HLL() : h(0) {}
	HLL(ull x) : h(x%mod) {}
	ull h;
	HLL& operator+=(const HLL& o){
		h = (h+o.h);
		if(h>=mod)h-=mod;
		return *this;
	}
	HLL operator+(const HLL& o)const{
		return HLL(*this)+=o;
	}
	HLL& operator-=(const HLL& o){
		h = (mod+h-o.h);
		if(h>=mod)h-=mod;
		return *this;
	}
	HLL operator-(const HLL& o)const{
		return HLL(*this)-=o;
	}
	// multiplication by fast exponentation
	HLL operator*(const HLL& o)const{
		return fpow(*this, (ull)o, _1 + _2, HLL(0));
	}
	HLL& operator*=(const HLL& o){
		*this = *this * o;
		return *this;
	}
	HLL& operator/=(const HLL& o){
		//ASS(millerRabin(mod));
		return (*this)*=fpow(o, mod-2, _1 * _2, HLL(1));
	}
	HLL operator/(const HLL& o)const{
		return HLL(*this)/=o;
	}
	
	HLL& operator--(){
		if(h==0)h=mod-1;
		else --h;
	}
	HLL& operator++(){
		if(h==mod-1)h=0;
		else ++h;
	}

	/*
	bool operator==(const H1& o)const{
		return h1==o.h1;
	}

	bool operator!=(const H1& o)const{
		return !operator==(o);
	}*/

	operator ull()const{
		return h;
	}
};






// 2 ints + 1 long long
template<int mod1 = (1u<<31)-1, int mod2 = (1u<<31)-19>
struct SuperHash2{
	SuperHash2() : h1(0), h2(0), h(0) {}
	SuperHash2(int x) : h1(x%mod1), h2(x%mod2), h(x) {}
	ui32 h1,h2;
	ull h;
	SuperHash2& operator+=(const SuperHash2& o){
		h1 += o.h1;
		h2 += o.h2;
		if(h1>=mod1) h1-=mod1;
		if(h2>=mod2) h2-=mod2;
		h += o.h;
		return *this;
	}
	SuperHash2 operator+(const SuperHash2& o)const{
		return SuperHash2(*this)+=o;
	}
	SuperHash2& operator-=(const SuperHash2& o){
		h1 += mod1-o.h1;
		h2 += mod2-o.h2;
		if(h1>=mod1) h1-=mod1;
		if(h2>=mod2) h2-=mod2;
		h -= o.h;
		return *this;
	}
	SuperHash2 operator-(const SuperHash2& o)const{
		return SuperHash2(*this)-=o;
	}
	SuperHash2& operator*=(const SuperHash2& o){
		h1 = (1ULL*h1*o.h1)%mod1;
		h2 = (1ULL*h2*o.h2)%mod2;
		h *= o.h;
		return *this;
	}
	SuperHash2 operator*(const SuperHash2& o)const{
		return SuperHash2(*this)*=o;
	}

	bool operator==(const SuperHash2& o)const{
		return h1==o.h1 and h2==o.h2 and h==o.h;
	}

	bool operator!=(const SuperHash2& o)const{
		return !operator==(o);
	}
};








// 3 ints + 1 long long
template<int mod1 = (1u<<31)-1, int mod2 = (1u<<31)-19, int mod3 = (1u<<31)-69>
struct SuperHash3{
	SuperHash3() : h1(0), h2(0), h3(0), h(0) {}
	SuperHash3(int x) : h1(x%mod1), h2(x%mod2), h3(x%mod3), h(x) {}
	ui32 h1,h2,h3;
	ull h;
	SuperHash3& operator+=(const SuperHash3& o){
		h1 += o.h1;
		h2 += o.h2;
		h3 += o.h3;
		if(h1>=mod1) h1-=mod1;
		if(h2>=mod2) h2-=mod2;
		if(h3>=mod3) h3-=mod3;
		h += o.h;
		return *this;
	}
	SuperHash3 operator+(const SuperHash3& o)const{
		return SuperHash3(*this)+=o;
	}
	SuperHash3& operator-=(const SuperHash3& o){
		h1 += mod1-o.h1;
		h2 += mod2-o.h2;
		h3 += mod3-o.h3;
		if(h1>=mod1) h1-=mod1;
		if(h2>=mod2) h2-=mod2;
		if(h3>=mod3) h3-=mod3;
		h -= o.h;
		return *this;
	}
	SuperHash3 operator-(const SuperHash3& o)const{
		return SuperHash3(*this)-=o;
	}
	SuperHash3& operator*=(const SuperHash3& o){
		h1 = (1ULL*h1*o.h1)%mod1;
		h2 = (1ULL*h2*o.h2)%mod2;
		h3 = (1ULL*h3*o.h3)%mod3;
		h *= o.h;
		return *this;
	}
	SuperHash3 operator*(const SuperHash3& o)const{
		return SuperHash3(*this)*=o;
	}

	bool operator==(const SuperHash3& o)const{
		return h1==o.h1 and h2==o.h2 and h3==o.h3 and h==o.h;
	}

	bool operator!=(const SuperHash3& o)const{
		return !operator==(o);
	}
};










// dynamic hash
struct H1X{
	H1X(int mod) : mod1(mod), h1(0) {}
	H1X(int mod, int x) : mod1(mod), h1(x%mod1) {}
	//H1X(const H1X& o) : mod1(o.mod1), h1(o.h1) {}
	H1X& operator=(const H1X& o){
		ASS(mod1==o.mod1);
		//mod1 = o.mod1;
		h1 = o.h1;
		return *this;
	}
	const int mod1;
	ui32 h1;
	H1X& operator+=(const H1X& o){
		ASS(mod1==o.mod1);
		h1 = (h1+o.h1)%mod1;
		return *this;
	}
	H1X operator+(const H1X& o)const{
		return H1X(*this)+=o;
	}
	H1X& operator-=(const H1X& o){
		ASS(mod1==o.mod1);
		h1 = (mod1+h1-o.h1)%mod1;
		return *this;
	}
	H1X operator-(const H1X& o)const{
		return H1X(*this)-=o;
	}
	H1X& operator*=(const H1X& o){
		ASS(mod1==o.mod1);
		h1 = (1ULL*h1*o.h1)%mod1;
		return *this;
	}
	H1X operator*(const H1X& o)const{
		return H1X(*this)*=o;
	}
	H1X& operator/=(const H1X& o){
		ASS(mod1==o.mod1);
		//ASS(millerRabin(mod1));
		return (*this)*=fpow(o,mod1-2, (_1 * _2), H1X(mod1,1));
	}
	H1X operator/(const H1X& o)const{
		return H1X(*this)/=o;
	}

	/*
	bool operator==(const H1X& o)const{
		return h1==o.h1;
	}

	bool operator!=(const H1X& o)const{
		return !operator==(o);
	}*/

	operator ui32()const{
		return h1;
	}

	template<class T>
	explicit operator T()const{
		return h1;
	}
};


template<class INT> H1X operator/(const H1X& h, const INT& i){ ASS(h.mod1);
	return h / H1X(h.mod1,i);
}
template<class INT> H1X operator/(const INT& i, const H1X& h){ ASS(h.mod1);
	return H1X(h.mod1,i) / h;
}

template<class INT> H1X operator*(const H1X& h, const INT& i){ ASS(h.mod1);
	return h * H1X(h.mod1,i);
}
template<class INT> H1X operator*(const INT& i, const H1X& h){ ASS(h.mod1);
	return H1X(h.mod1,i) * h;
}

template<class INT> H1X operator+(const H1X& h, const INT& i){ ASS(h.mod1);
	return h + H1X(h.mod1,i);
}
template<class INT> H1X operator+(const INT& i, const H1X& h){ ASS(h.mod1);
	return H1X(h.mod1,i) + h;
}

template<class INT> H1X operator-(const H1X& h, const INT& i){ ASS(h.mod1);
	return h - H1X(h.mod1,i);
}
template<class INT> H1X operator-(const INT& i, const H1X& h){ ASS(h.mod1);
	return H1X(h.mod1,i) - h;
}



}



#if __cplusplus >= 201103L or defined _MSC_VER
#include <unordered_map>
namespace std{
#else
#include <ext/hash_map>
namespace __gnu_cxx{
#endif

template<int h1, int h2> struct hash<ab::H2<h1,h2> >{
	size_t operator()(const ab::H2<h1,h2>& h)const{
		return h.h1^h.h2;
	}
};
template<int h1> struct hash<ab::H1<h1> >{
	size_t operator()(const ab::H1<h1>& h)const{
		return h.h1;
	}
};

}



















////////////////////////////////////////////////////////////////////////////////
//                                                                            //
//  ACTUAL SOLUTION IS AT THE END OF THIS FILE!!!                             //
//                                                                            //
////////////////////////////////////////////////////////////////////////////////


















////////////////////////// PROTOTYPING TEMPLATE /////////////////////////////////
//
// Implementation: Adam Blaszkiewicz (atablash.pl), 2012-2014
/*
    This program is licensed under GNU General Public License version 3.
    See <http://www.gnu.org/licenses/>.
*/
//
//

// enable c++ iostream; only if no fastio
//#define IOSTREAM

//#define NO_UNLOCKED	// fread_unlocked, fwrite_unlocked



// PRIi64, PRIui64
#define __STDC_FORMAT_MACROS
#include<inttypes.h>



//#if MIN_GCC(4,1,3)
//#include<bits/stdc++.h>
//#else
#include<vector>
#include<map>
#include<queue>
#include<algorithm>
#include<string>
#include<stdint.h>
#include<cstring>
#include<iostream>
#include<set>
#include<climits>
#include<bitset>
#include<limits>
#include<sstream>
#include<cmath>
//#endif








/*
#define fo3(i,a,b) for(int i=(int)(a); i<(int)(b); ++i)
#define of3(i,a,b) for(int i=(int)((b)-1); i>=(int)(a); --i)

#define fo2(i,n) fo3(i,0,n)
#define of2(i,n) of3(i,0,n)

#define fo(...) VA_SEL(fo,__VA_ARGS__)
#define of(...) VA_SEL(of,__VA_ARGS__)
*/

#define inl		inline __attribute__ ((always_inline))
#define ninl	__attribute__ ((noinline))







#ifdef DEBUG_BUILD
	#undef FASTIO
#endif





#ifdef _WIN32

// TODO
#ifndef NO_UNLOCKED
#define NO_UNLOCKED
#endif

//#define fread_unlocked _fread_nolock
//#define fwrite_unlocked _fwrite_nolock

#endif



using namespace std;
using namespace __gnu_cxx;

namespace ab{}
using namespace ab;





template<class T>inline void sortu(T& t){t.resize(std::unique(ALL(t))-t.be);}


inline uint _rand(){
	if(RAND_MAX < (1<<15)) return (rand()<<15) | rand();
	else return rand();
}
#define RND _rand()


#define ri _rint()
#define rui _ruint()
#define rll _rll()
#define rull _rull()
#define rchar _rchar()
#define rstr _rstr()


#ifndef FASTIO
inline void _fin(int){}
inline void _fout(int){}
#ifdef IOSTREAM
inline int _rint(){int r;cin>>r;return r;}
inline uint _ruint(){uint r;cin>>r;return r;}
inline ull _rull(){ull r;cin>>r;return r;}
inline ll _rll(){ll r;cin>>r;return r;}
inline char _rchar(){return cin.get();}
inline string _rstr(){string s;cin>>s;return s;}
template<typename T>inline void W(const T& i){cout<<i; cout.flush();}
inline void W(){W('\n');}
#else
inline int _rint(){int r;scanf("%d",&r);return r;}
inline uint _ruint(){uint r;scanf("%u",&r);return r;}
inline ull _rull(){ull r;scanf("%" SCNu64,&r);return r;}
inline ull _rll(){ll r;scanf("%" SCNd64,&r);return r;}
inline char _rchar(){return getchar();}
inline string _rstr(){
	string s;
	char c=rchar;
	while(c!=-1 && !isgraph(c))c=rchar;
	for(;;){
		if(!isgraph(c))break;
		s+=c;
		c=rchar;
	}
	return s;
}
inline void W(char a='\n'){printf("%c",a);}
inline void W(const string&s){printf("%s",s.c_str());}
inline void W(int a){printf("%d",a);}
inline void W(uint a){printf("%u",a);}
inline void W(const ui64& a){printf("%" PRIu64,a);}
inline void W(const i64& a){printf("%" PRIi64,a);}
inline void W(const char *str){fputs(str,stdout);}
inline void W(const double& d){printf("%.20f",d);}
inline void W(const long double& d){printf("%.50Lf",d);}
#endif
#else

#ifndef NO_UNLOCKED
#define FREAD fread_unlocked
#define FWRITE fwrite_unlocked
#else
#define FREAD fread
#define FWRITE fwrite
#endif

// todo: test on pointers
const int _IB=32768;const int _OB=32768;
char _iB[_IB];int _iP = _IB;
char _oB[_OB];int _oP = 0;
inline void _fin(int mc){
	int r=_IB-_iP;
	if(r>mc)return;
	FOR(i,r) _iB[i]=_iB[i+_iP];	// TODO: try memcpy
    int rd=FREAD(_iB+r,1,_iP,stdin);
	if(rd!=_iP) _iB[r+rd]=0;
	_iP = 0;
}
inline void _fout(int mc){
	if(_OB-_oP>mc)return;
	FWRITE(_oB,1,_oP,stdout);
	_oP = 0;
}
inline void _W(char c='\n'){_oB[_oP++]=c;} // unchecked!
inline char _rc(){return _iB[_iP++];}
inline char _rchar(){_fin(1);return _rc();}
inline string _rstr(){
	string s;
	for(;;){
		char c=rchar;
		if(!isprint(c)||isspace(c))break;
		s+=c;
	}
	return s;
}
template<class T>inline T _rur(){ // unchecked!
    T r=0;char c=_rc();
    do c-='0',r=r*10+c,c=_rc();while(c>='0');
    return r;}
template<class T>inline T _rsi(){ // unchecked!
	char c=_rc();
	while(c<'-')c=_rc();
	if(c=='-')return -_rur<T>();
	else{--_iP;return _rur<T>();}}
template<class T>inline T _ru(){  // unchecked!
	while(_rc()<'0');--_iP;
	return _rur<T>();
}

inline int _rint(){_fin(15);return _rsi<int>();}
inline uint _ruint(){_fin(15);return _ru<uint>();}
inline ll _rll(){_fin(25);return _rsi<ll>();}
inline ull _rull(){_fin(25);return _ru<ull>();}

const int _rs = 20; char _r[_rs];
template<class T>inline void _w(T i){	// unchecked!
	if(numeric_limits<T>::is_signed and i<0) _W('-'), i=-i;
	else if(i==0){_W('0'); return;}
	int pos = _rs;
	do _r[--pos]='0'+i%10, i/=10; while(i);
	do _W(_r[pos++]); while(pos<_rs);
}
inline void W(const char c){_fout(2);_W(c);}
inline void W(const int32_t& i){_fout(15);_w(i);}
inline void W(const uint32_t& i){_fout(15);_w(i);}
inline void W(const int64_t& i){_fout(25);_w(i);}
inline void W(const uint64_t& i){_fout(25);_w(i);}
inline void W(const char*str, int l){
	for(int b=0; b<l; b+=_OB){
		int num = min(_OB,l-b);
		_fout(num);
		memcpy(&_oB[_oP], str+b, num);
		_oP+=num;
	}
}
inline void W(const char*str){W(str,strlen(str));}
inline void W(const string&s){W(s.c_str(),s.siz);}
inline void W(double d){_fout(50);_oP+=sprintf(&_oB[_oP],"%.20f",d);}	// todo
#endif
template<class A,class B>inline void W(const A&a,const B&b){W(a);W(b);}
template<class A,class B,class C>
inline void W(const A&a,const B&b,const C&c){W(a);W(b);W(c);}
template<class A,class B,class C,class DD>
inline void W(const A&a,const B&b,const C&c,const DD&dd){W(a);W(b);W(c);W(dd);}
template<class T>inline void sortall(T&t){sort(t.be,t.en);}
template<class T>inline void uniqall(T&t){t.resize(unique(t.be,t.en)-t.be);}


#define rgraph _rgraph()
inline char _rgraph(){char c;do c=rchar;while(!isgraph(c));return c;}

#define subset(a,b) (a&b==a)
#define kbegin(k) ((1<<k)-1)
#define kend(k,n) ((kbegin(k)<<n-k)+1)
inline uint knext(uint a){uint b=(a|(a-1))+1;return b|((a^b)>>(__builtin_ctz(a)+2));}
#define fors(x,k,n) for(uint x=kbegin(k);x<kend(k,n);x=knext(x))

struct _O{template<class T>_O&operator<(const T&_t){
		oc(1);W(_t);oc(0);
		return *this;
}}O;

struct _I{
	_I&operator>(int32_t&_t){_t=ri;return*this;}
	_I&operator>(uint32_t&_t){_t=rui;return*this;}
	_I&operator>(int64_t&_t){_t=rll;return*this;}
	_I&operator>(uint64_t&_t){_t=rull;return*this;}
	_I&operator>(char&_t){_t=rchar;return*this;}
	_I&operator>(string&_t){_t=rstr;return*this;}
}I;




inline void tc();
#ifdef GEN
int argc;  char **argv;
int main(int _argc, char *_argv[]){
	argc = _argc;  argv = _argv;
	if(argc<2){
		O < "Usage: " < argv[0] < " NR_TESTU" < N;
		return 1;
	}
	srand(atoi(argv[1]));
#else
int main(){
#endif

	//Log log;
	//log.autoFlush = true;
	//Log::global() = &log;

#ifdef FASTIO
    setvbuf(stdin,0,_IONBF,0);setvbuf(stdout,0,_IONBF,0);
#elif defined IOSTREAM
	ios_base::sync_with_stdio(0);cout.precision(10);cout.setf(ios::fixed,ios::floatfield);
	#if not defined DEBUG_BUILD and not defined COLOR_CONSOLE
	cin.tie(0);
	#endif
#endif

#ifdef DEBUG_BUILD
#ifdef _WIN32
	ec(0);
	oc(0);
#else
// TODO: *nix
#endif
#endif
	
#ifdef READ_NUM_TEST_CASES
	int nz=rui;FOR(i,nz)
#endif
	tc();
#ifdef FASTIO
    FWRITE(_oB,1,_oP,stdout);
#endif
	return 0;
}
// END OF TEMPLATE





































////////////////////////////////////////////////////////////////////////////////
//                                                                            //
//  ACTUAL SOLUTION BEGINS HERE:                                              //
//                                                                            //
////////////////////////////////////////////////////////////////////////////////

#include "poszukiwania.h"
#include "message.h"





typedef SuperHash3<> H;
//typedef SuperHash2<> H;
//typedef H2<> H;

// meta
int numberOfNodes;
int myNodeId;

// input
int textSize;
int pattSize;


// common
const int base = 1000000117;

int numPrzylozenia;
int przylozeniaPerNode;

H patternHash;

inline int seqAt(int i){
	return SeqAt(i+1)+1;
}

inline int signalAt(int i){
	return SignalAt(i+1)+1;
}


const int maxMessageSize = 256 * 1024;

const int hashSize = 3*4 + 8; // !!!
inline void putHash(int target, const H& value){
	PutInt(target, value.h1);
	PutInt(target, value.h2);
	PutInt(target, value.h3);
	PutLL(target, value.h);
}

inline H getHash(int from){
	H h;
	h.h1 = GetInt(from);
	h.h2 = GetInt(from);
	h.h3 = GetInt(from);
	h.h = GetLL(from);
	return h;
}


// instance 0
int numTextPrefsumBlocks;
int textPrefsumBlockSize;
int blocksPerNode;
vector<H> textPrefsumSparse;
//ull textPrefsumSparse2[1010000000 / textPrefsumBlockSize];


// worker


inline pii getPrefsumFragmentBounds(int iBlock){
	int fr = iBlock*textPrefsumBlockSize;
	int to = (iBlock+1)*textPrefsumBlockSize;
	if(to >= textSize) to = textSize;
	if(fr>to) fr = to;
	return mp(fr,to);
}

void workerComputePrefsumFragment(){
	textPrefsumBlockSize = sqrt(textSize);
	if(textPrefsumBlockSize <= 0) textPrefsumBlockSize = 1;
	numTextPrefsumBlocks = (textSize + textPrefsumBlockSize - 1) / textPrefsumBlockSize;
	
	if(myNodeId==0) E < "prefsum block size: " < textPrefsumBlockSize < NL;
	
	
	blocksPerNode = (numTextPrefsumBlocks + numberOfNodes - 1) / numberOfNodes;
	
	int messageSize = 0;
	
	FOR(i,blocksPerNode){
		int iBlock = blocksPerNode*myNodeId + i;
		pii bounds = getPrefsumFragmentBounds(iBlock);
		if(bounds.fi == bounds.se) break;
		
		H cHash = 0;
		H basePow = fpow((H)base, bounds.fi);
		FO(j, bounds.fi, bounds.se){
			cHash += basePow * seqAt(j);
			basePow *= base;
		}
		E < "computed hash " < cHash.h1 < " for block " < iBlock < NL;
		
		if(messageSize + hashSize > maxMessageSize){
			Send(0);
			messageSize = 0;
		}
		putHash(0,cHash);
		messageSize += hashSize;
	}
	Send(0);
}


void masterSendPrefsums(){
	if(myNodeId != 0) return;
	
	textPrefsumSparse.resize(numTextPrefsumBlocks+1);
	
	// receive prefsum fragments
	//FOR(kk,numberOfNodes){
		//int fromNode = Receive(-1);
	FOR(fromNode,numberOfNodes){
		Receive(fromNode);
		int messageSize = 0;
		
		FOR(i,blocksPerNode){
			int iBlock = blocksPerNode*fromNode + i;
			pii bounds = getPrefsumFragmentBounds(iBlock);
			if(bounds.fi == bounds.se) break;
			
			if(messageSize + hashSize > maxMessageSize){
				Receive(fromNode);
				messageSize = 0;
			}
			
			H h = getHash(fromNode);
			messageSize += hashSize;
			textPrefsumSparse[iBlock+1] = h;
		}
	}
	FOR(i,numTextPrefsumBlocks) textPrefsumSparse[i+1] += textPrefsumSparse[i];
	
	// send required prefsums
	FOR(iNode,numberOfNodes){
		int przylozenie = przylozeniaPerNode*iNode;
		int fullBlocks = przylozenie / textPrefsumBlockSize;
		int fullBlocks2 = (przylozenie + pattSize) / textPrefsumBlockSize;
		putHash(iNode, textPrefsumSparse[fullBlocks]);
		putHash(iNode, textPrefsumSparse[fullBlocks2]);
		Send(iNode);
	}
}


inline void tc(){
	numberOfNodes = NumberOfNodes();
	myNodeId = MyNodeId();
	
	textSize = SeqLength();
	pattSize = SignalLength();
	
	numPrzylozenia = textSize-pattSize+1;
	przylozeniaPerNode = (numPrzylozenia+numberOfNodes-1) / numberOfNodes;
	
	// compute prefsums
	workerComputePrefsumFragment();
	masterSendPrefsums();
	
	if(myNodeId==0) E < "prefsums computed" < NL;
	
	// compute pattern hash
	patternHash = 0;
	OF(i,0,pattSize){
		patternHash *= base;
		patternHash += signalAt(i);
	}
	
	if(myNodeId==0) E < "pattern hash computed. " < patternHash.h1 < NL;
	
	int fr = myNodeId*przylozeniaPerNode;
	int to = fr + przylozeniaPerNode;
	
	Receive(0);
	H prefsumLeft = getHash(0);
	H prefsumRight = getHash(0);
	
	//if(myNodeId==0) cerr << "prefsums sent" << endl;
	
	int iLeft = fr / textPrefsumBlockSize * textPrefsumBlockSize;
	H basePowLeft = fpow((H)base,iLeft);
	FO(i, iLeft, fr){
		prefsumLeft += basePowLeft * seqAt(i);
		basePowLeft *= base;
	}
	
	int iRight = (fr + pattSize) / textPrefsumBlockSize * textPrefsumBlockSize;
	H basePowRight = fpow((H)base,iRight);
	FO(i, iRight, fr + pattSize){
		prefsumRight += basePowRight * seqAt(i);
		basePowRight *= base;
	}
	
	patternHash *= fpow((H)base, fr);
	
	int result = 0;
	
	FO(i, fr, to){
		if(i >= numPrzylozenia)break;
		
		// check przylozenie 'i'
		H candHash = prefsumRight - prefsumLeft;
		E < "position " < i < ":  candHash==" < candHash.h1
			< "  patternHash==" < patternHash.h1 < NL;
		if(candHash == patternHash){
			E < "match at position " < i < NL;
			++result;
		}
		
		if(i < to-1){
			prefsumLeft += basePowLeft * seqAt(i);
			prefsumRight += basePowRight * seqAt(i+pattSize);
			
			basePowLeft *= base;
			basePowRight *= base;
			patternHash *= base;
		}
	}
	
	
	// collect result
	PutInt(0,result);
	Send(0);
	
	if(myNodeId==0){
		result = 0;
		FOR(kk,numberOfNodes){
			int fromNode = Receive(-1);
			result += GetInt(fromNode);
		}
		O < result < NL;
	}
}

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//#define READ_NUM_TEST_CASES
//#define ASSERTS		// force asserts on online judge
//#define FASTIO

//#define DEBUG_BUILD

//#include<atablash/splay/common.hpp>
//#include<atablash/splay/node.hpp>

//#include<atablash/interval-tree.hpp>






#include<stdint.h>

#include<utility>

#include<vector>
#include<memory>




// abbrevs

typedef unsigned int uint;

typedef int8_t i8;
typedef uint8_t ui8;
typedef int16_t i16;
typedef uint16_t ui16;
typedef int32_t i32;
typedef uint32_t ui32;
typedef int64_t i64;
typedef uint64_t ui64;

// old:
typedef i64 ll;
typedef ui64 ull;

typedef std::pair<i32,i32> pii;
typedef std::pair<double,double> pdd;

typedef std::vector<i32> vi;
#define VE std::vector

#define umap std::unordered_map
#define umultimap std::unordered_multimap
#define uset std::unordered_set
#define umultiset std::unordered_multiset

typedef unsigned short ushort;
typedef unsigned char uchar;


template<class T> using sptr = std::shared_ptr<T>;
template<class T> using uptr = std::unique_ptr<T>;
template<class A, class B> using p = std::pair<A, B>;



namespace ab{

struct Void {};


// convert to float with enough precision
template<typename I>struct FloatFrom{typedef Void R;};
template<>struct FloatFrom<i32>{typedef double R;};
template<>struct FloatFrom<ui32>{typedef double R;};
template<>struct FloatFrom<i64>{typedef long double R;};
template<>struct FloatFrom<ui64>{typedef long double R;};
template<>struct FloatFrom<i16>{typedef float R;};
template<>struct FloatFrom<ui16>{typedef float R;};
template<>struct FloatFrom<i8>{typedef float R;};
template<>struct FloatFrom<ui8>{typedef float R;};
template<>struct FloatFrom<float>{typedef float R;};
template<>struct FloatFrom<double>{typedef double R;};
template<>struct FloatFrom<long double>{typedef long double R;};

// get type capable of storing multiplication result
template<typename I>struct Double{typedef Void R;};
template<>struct Double<i8>{typedef i16 R;};
template<>struct Double<ui8>{typedef ui16 R;};
template<>struct Double<i16>{typedef i32 R;};
template<>struct Double<ui16>{typedef ui32 R;};
template<>struct Double<i32>{typedef i64 R;};
template<>struct Double<ui32>{typedef ui64 R;};

template<>struct Double<float>{typedef float R;};
template<>struct Double<double>{typedef double R;};
template<>struct Double<long double>{typedef long double R;};



#if defined __GNUC__ && ( defined __x86_64__ || defined __ppc64__ || defined __MINGW64__ )
typedef __int128_t i128;
typedef __uint128_t ui128;
template<>struct Double<i64>{typedef i128 R;};
template<>struct Double<ui64>{typedef ui128 R;};
#endif


}


// enable debug if any debug macro is defined
#if (defined _DEBUG || defined DEBUG) && !defined DEBUG_BUILD
#define DEBUG_BUILD
#endif

// DEBUG_BUILD (set or not set) overrides NDEBUG
#ifdef DEBUG_BUILD
	#undef NDEBUG
	//#pragma message "Compiling in DEBUG mode."
#else
	#ifndef NDEBUG
	#define NDEBUG
	#endif
#endif

//#include <cstdio>
//#include <cfloat>




//#include<type_traits>


#define _CAT(a,b) a##b
#define CAT(a,b) _CAT(a,b)
#define _10TH(a,b,c,d,e,f,g,h,i,X,...) X
#define VA_CNT(...) _10TH(__VA_ARGS__,9,8,7,6,5,4,3,2,1,0)
#define VA_SEL(a,...) CAT(a,VA_CNT(__VA_ARGS__))(__VA_ARGS__)

#define _VA_GTONE(...) _10TH(__VA_ARGS__,1,1,1,1,1,1,1,1,0,0)
#define VA_GTONE(a,...) CAT(a,_VA_GTONE(__VA_ARGS__))(__VA_ARGS__)


#define MIN_GCC(a,b,c) (__GNUC__ > (a) || \
              (__GNUC__ == (a) && (__GNUC_MINOR__ > (b) || \
                                 (__GNUC_MINOR__ == (b) && \
								 __GNUC_PATCHLEVEL__ >= (c)))))





// TODO: po co to bylo??
/*
#include<functional>
#if __cplusplus >= 201103L
namespace std
{
    template<class T>
    struct hash
    {
        typedef T argument_type;
        typedef typename std::underlying_type< argument_type >::type underlying_type;
        typedef typename std::hash< underlying_type >::result_type result_type;
        result_type operator()( const argument_type& arg ) const
        {
            std::hash< underlying_type > hasher;
            return hasher( static_cast< underlying_type >( arg ) );
        }
    };
}
#endif
*/


#define bac back()
#define fro front()
#define emp empty()
#define fi first
#define se second
#define siz size()
#define ins insert
#define era erase
#define mp make_pair
#define be begin()
#define en end()
#define rbe rbegin()
#define ren rend()
#define pub push_back
#define puf push_front
#define pob pop_back()
#define pof pop_front()
#define bs binary_search
#define lb lower_bound
#define ub upper_bound
#define pq priority_queue
#define si (int)


#undef FO
#undef OF

#define FOR(i,n) for(int i=0; i<(int)(n); ++i)
#define FO(i,a,b) for(int i=(a); i<(int)(b); ++i)
#define OF(i,a,b) for(int i=(int)(b)-1;i>=(int)(a);--i)
#define FE(it,c)  for(__typeof((c).begin()) it=(c).begin(); it!=(c).end(); ++it)
#define FER(it,c) for(__typeof((c).begin()) it=(c).begin(); it!=(c).end(); )
#define ALL(c) (c).begin(),(c).end()
#define ZERO(c) memset(c,0,sizeof(c))

#define AU(v,val) __typeof(val) v(val)

const char NL='\n';
const char SP=' ';






// Visual C++ intristics
#ifdef _MSC_VER
	#include <intrin.h>
	#define __builtin_popcount __popcnt

	#ifdef _WIN64
		#define __builtin_popcountll __popcnt64
	#else
		inline int __builtin_popcountll(__int64 a){ return __builtin_popcount((ui32)a) + __builtin_popcount(a >> 32); }
	#endif 
#endif


// Visual C++ 'and', 'or', 'not'
#ifdef _MSC_VER
	#define and &&
	#define or ||
	#define not !
#endif


namespace ab{

template<class T>inline T cbitl(T x,int i){return (x<<i) ^ (x>>(sizeof(T)*8-i));} // cycle bits left
inline int popcount(uint i){return __builtin_popcount(i);}
inline int popcount(ull i){return __builtin_popcountll(i);}

#ifdef __GNUC__
inline int parity(uint i){return __builtin_parity(i);}
inline int parity(ull i){return __builtin_parityll(i);}
inline int ilog2(uint i){return 31-__builtin_clz(i);} // int log; floor(log2(i))
inline int ilog2(ull i){return 63-__builtin_clzll(i);}
#endif


template<class T>inline bool isPowerOf2(const T&x){return !(x&(x-1));}



struct Static{
	Static() = default;
	Static(const Static&) = delete;
	Static(Static&&) = delete;
	Static(const Static&&) = delete;
	Static& operator=(const Static&) = delete;
	Static& operator=(Static&&) = delete;
	Static& operator=(const Static&&) = delete;
};



}






#include<vector>
#include<unordered_map>


// ?
#include<iostream>
#include<fstream>
#include<string>
#include<algorithm>
#include<mutex>

// to_string fix for MinGW





#include<map>
#include<iostream>



#if __cplusplus >= 201103L or defined _MSC_VER
#include <unordered_map>
#include <unordered_set>
namespace std{
#else
#include <ext/hash_map>
#include <ext/hash_set>
namespace __gnu_cxx{
#define unordered_map hash_map
#define unordered_multimap hash_multimap
#define unordered_set hash_set
#define unordered_multiset hash_multiset
/*
template<class K, class V> class unordered_map : public hash_map<K,V>{
public:
	typename hash_map<K,V>::iterator erase(const typename hash_map<K,V>::iterator& it){
		typename hash_map<K,V>::iterator r = it;
		++r;
		if(r!=hash_map<K,V>::end()){
			K key = r->first;
			hash_map<K,V>::erase(it);
			return hash_map<K,V>::find(key);
		}
		else{
			hash_map<K,V>::erase(it);
			return r;
		}
	}
	typename hash_map<K,V>::size_type erase(const K& key){
		return hash_map<K,V>::erase(key);
	}
};
*/
#endif

// 1,2,last (!!!!!)
/*template<>*/ template<class A,class B>struct hash<std::map<A,B> >{
    size_t operator()(const std::map<A,B>& m) const{
        size_t r = m.size();
        if(!r)return 0;
        __typeof(m.begin()) i=m.be;
        r^=hash<__typeof(i)>()(i);
        ++i;
        r^=cbitl(hash<__typeof(i)>()(*i),sizeof(r)*8/4);
        i=m.end();
        --i;
        r^=cbitl(hash<__typeof(i)>()(*i),sizeof(r)*8/2);
        return r;
    }
};



// hash pairs:
/*template<>*/ template<class A, class B>struct hash<pair<A,B> >{
    size_t operator()(const pair<A,B>& p) const{
        return hash<A>()(p.first) ^ ab::cbitl(hash<B>()(p.second),sizeof(size_t)*8/2);
    }
};



// hash enums:
//
// TODO: fix for msvc
#if defined __GNUC__ and MIN_GCC(4,8,4)
template<class E> struct hash {
    using sfinae = typename std::enable_if<std::is_enum<E>::value, E>::type;
public:
    size_t operator()(const E&e) const {
      return std::hash<typename std::underlying_type<E>::type>()((typename std::underlying_type<E>::type)e);
    }
};
#endif
  
} // namespace std / __gnu_cxx








// component-wise pair operators
template<class A, class B, class C, class D>
inline std::pair<A,B>& operator+=(std::pair<A,B>& p, const std::pair<C,D>& o){
	p.first+=o.first;
	p.second+=o.second;
	return p;
}
template<class A, class B, class C, class D>
inline std::pair<A,B>& operator-=(std::pair<A,B>& p, const std::pair<C,D>& o){
	p.first-=o.first;
	p.second-=o.second;
	return p;
}
template<class A, class B, class C, class D>
inline std::pair<A,B>& operator*=(std::pair<A,B>& p, const std::pair<C,D>& o){
	p.first*=o.first;
	p.second*=o.second;
	return p;
}
template<class A, class B, class C, class D>
inline std::pair<A,B>& operator/=(std::pair<A,B>& p, const std::pair<C,D>& o){
	p.first/=o.first;
	p.second/=o.second;
	return p;
}

template<class Afi, class Ase, class Bfi, class Bse>
inline std::pair<decltype(Afi() + Bfi()), decltype(Ase() + Bse())>&
operator+(const std::pair<Afi,Ase>& a, const std::pair<Bfi,Bse>& b){
	return std::make_pair(a.fi+b.fi, a.se+b.se);
}
template<class Afi, class Ase, class Bfi, class Bse>
inline std::pair<decltype(Afi() - Bfi()), decltype(Ase() - Bse())>&
operator-(const std::pair<Afi,Ase>& a, const std::pair<Bfi,Bse>& b){
	return std::make_pair(a.fi-b.fi, a.se-b.se);
}
template<class Afi, class Ase, class Bfi, class Bse>
inline std::pair<decltype(Afi()*Bfi()), decltype(Ase()*Bse())>&
operator*(const std::pair<Afi,Ase>& a, const std::pair<Bfi,Bse>& b){
	return std::make_pair(a.fi*b.fi, a.se*b.se);
}
template<class Afi, class Ase, class Bfi, class Bse>
inline std::pair<decltype(Afi() / Bfi()), decltype(Ase() / Bse())>&
operator/(const std::pair<Afi,Ase>& a, const std::pair<Bfi,Bse>& b){
	return std::make_pair(a.fi/b.fi, a.se/b.se);
}








// vector operators
template<class T, class U>
inline std::vector<T>& operator+=(std::vector<T>& v, const std::vector<U>& o){
	ASS(v.siz == o.siz);
	FOR(i,v.siz) v[i] += o[i];
	return v;
}


template<class T>
inline std::vector<T>& operator*=(std::vector<T>& v, const T& a){
	FOR(i,v.siz) v[i] *= a;
	return v;
}





// serialization
template<class A,class B>inline std::ostream&operator<<(std::ostream&o,const std::pair<A,B>&p){o<<'<'<<p.first<<", "<<p.second<<'>';return o;}
template<class A,class B>inline std::ostream&operator<<(std::ostream&o,const std::map<A,B>&m){o<<'\n';FE(k,m)o<<"map["<<k->first<<"] -> "<<k->se<<'\n';return o;}
template<class A,class B>inline std::ostream&operator<<(std::ostream&o,const umap<A,B>&m){o<<'\n';FE(k,m)o<<"umap["<<k->first<<"] -> "<<k->se<<'\n';return o;}
template<class A,class B>inline std::ostream&operator<<(std::ostream&o,const uset<A,B>&_m){o<<"uset{\n";FE(k,_m)o<<*k<<'\n';o<<'\n';return o;}
template<class A>inline std::ostream&operator<<(std::ostream&o,const std::vector<A>&_v){o<<'\n';FOR(i,_v.siz)o<<"vector["<<i<<"] = "<<_v[i]<<"}\n";return o;}





// fix for MinGW: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=52015
#ifdef _GLIBCXX_HAVE_BROKEN_VSWPRINTF
namespace std{
	template<class T>
	inline string to_string(const T& t){
		stringstream ss;
		ss << t;
		return ss.str();
	}
}
#endif





//#define  LOG0(str) 			fprintf(stderr,"%s:%d - " str "\n",__FILE__,__LINE__)
//#define  LOG1(str,...)		fprintf(stderr,"%s:%d - " str "\n",__FILE__,__LINE__,__VA_ARGS__)
//#define LOG(...) VA_GTONE(LOG,__VA_ARGS__)


#define LOGD(str) if(ab::Log::global()) ab::Log::global()->debug(str,__FILE__,__LINE__)
#define LOGI(str) if(ab::Log::global()) ab::Log::global()->info(str,__FILE__,__LINE__)
#define LOGW(str) if(ab::Log::global()) ab::Log::global()->warning(str,__FILE__,__LINE__)
#define LOGE(str) if(ab::Log::global()) ab::Log::global()->error(str,__FILE__,__LINE__)
#define LOGF(str) if(ab::Log::global()) ab::Log::global()->fail(str,__FILE__,__LINE__)

	


namespace ab{


// TODO: czas logowania
// TODO: interfejs do dodawania nazw message levelom, ustawiania nazwy pliku z logiem, czy printowac na stderr, ...
//
// level >= DEBUG powoduje ignorowanie logowania w release
class Log{
public:
	enum{
		DEBUG = 5000,
		INFO = 4000, // default?
		WARNING = 3000,
		ERROR = 2000,
		FAIL = 1000};

public:
	void debug(const std::string& _message, const std::string& file="", int line=0){
		message(DEBUG, _message, file, line);
	}
	void info(const std::string& _message, const std::string& file = "", int line = 0){
		message(INFO, _message, file, line);
	}
	void warning(const std::string& _message, const std::string& file = "", int line = 0){
		message(WARNING, _message, file, line);
	}
	void error(const std::string& _message, const std::string& file = "", int line = 0){
		message(ERROR, _message, file, line);
	}
	void fail(const std::string& _message, const std::string& file = "", int line = 0){
		message(FAIL, _message, file, line);
	}

	// slow
	void flushConsole(){
		// avoid slow cout during lock
		// copy messages to print
		static const uint max_messages_flush = 128;
		std::vector<Message> messages_copy;
		{
			std::lock_guard<std::mutex> lock(mut);
			messages_copy.assign(messages.begin() + numPrinted, messages.begin() + numPrinted + std::min(max_messages_flush, (uint)messages.size() - numPrinted));
		}

		for (uint i = 0; i < messages_copy.size(); ++i){
			std::cout << messageToString(messages_copy[i]) << '\n';
		}
		std::cout.flush();

		numPrinted += messages_copy.size();
	}

	void message(int level, const std::string& messageText, const std::string& file = "", int line = 0){

		#if !defined DEBUG_BUILD
			if (level >= DEBUG) return;
		#endif
		
		std::lock_guard<std::mutex> lock(mut);

		messages.push_back(Message{ level, messageText, file, line });
		
		//if(autoFlush) flushConsole();

		#ifdef DEBUG_BUILD
			if (level <= ERROR){
				#ifdef _MSC_VER
					__debugbreak();
				#endif
				#ifdef __GNUC__
					__builtin_trap();
				#endif
			}
		#endif

	}


	// reference to pointer. client should create the log himself
	static Log*& global(){
		static Log* log = nullptr;
		return log;
	}

public:
	Log(){
		levelNames[DEBUG] = "DEBUG";
		levelNames[INFO] = "INFO";
		levelNames[WARNING] = "WARNING";
		levelNames[ERROR] = "ERROR";
		levelNames[FAIL] = "FAIL";
	}
	~Log(){
		if (filename != ""){
			std::ofstream os(filename);
			for (auto&m : messages){
				os << messageToString(m) << '\n';
			}
		}
	}
	
	//bool autoFlush = false;

private:
	struct Message{
		int level;
		std::string text;
		std::string file;
		int line;
	};
	
	static std::string shortenPath(const std::string& s){
		std::string result = s;
		std::string ss[] = {"include/", "include\\", "src/", "src\\"};
		for(uint i=0; i<sizeof(ss)/sizeof(std::string); ++i){
			auto pos = result.rfind(ss[i]);
			if(pos == std::string::npos) continue;
			
			result = result.substr(pos + ss[i].size(), std::string::npos);
		}
		return result;
	}

	std::string messageToString(const Message& m) const {
		std::string levelName;
		auto r = levelNames.find(m.level);
		if (r == levelNames.end()) levelName = std::to_string(m.level);
		else levelName = r->second;
		std::string result = levelName + ": " + m.text;
		if (m.file != "") result += " at " + shortenPath(m.file) + ":" + std::to_string(m.line);
		return result;
	}

	uint numPrinted = 0;
	std::vector<Message> messages;
	std::mutex mut; // TODO: spinlock

	std::unordered_map<int, std::string> levelNames;
	std::string filename = "atablash.log";

private:
	Log(const Log&) = delete;
	Log& operator=(const Log&) = delete;
};










}





inline void breakpoint(){}
#ifdef NDEBUG
	#define DE if(0)
#else // DEBUG
	#define DE
#endif


#if defined NDEBUG && not defined ASSERTS
	#define ASS(x)
	#define FLOAT_OK(x)
	#define ASSERT_FLOAT(x)
#else
	#include<cassert>
	#define ASS(x) assert(x)
	#define FLOAT_OK(x) ((x) <= LDBL_MAX && (x) >= -LDBL_MAX)
	#define ASSERT_FLOAT(f) ASS(FLOAT_OK(f))
#endif

#define DV(x) (E<#x<": "<(x)<N)
#define XX E<"XX at line "<__LINE__<NL;


#if defined DEBUG_BUILD or defined COLOR_CONSOLE
	#ifdef _WIN32
	
		#ifndef NOMINMAX
		#define NOMINMAX
		#endif
		
		#ifndef WIN32_LEAN_AND_MEAN
		#define WIN32_LEAN_AND_MEAN
		#endif
		
		#include<windows.h>
		inline void ec(int a){static HANDLE h=GetStdHandle(-12);SetConsoleTextAttribute(h,a?12:0xf);}	// color 12
		inline void oc(int a){static HANDLE h=GetStdHandle(-11);SetConsoleTextAttribute(h,a?10:0xf);}	// color 10
	#else
		// *nix includes for debug
	#endif
#else
	#define ec(x)
	#define oc(x)
#endif



#include <iostream>
struct _E{template<class T>_E&operator<(const T&_t){DE{ec(1);std::cerr<<_t;ec(0);}return*this;}};





#ifdef __GNUC__
	#pragma GCC diagnostic push
	#pragma GCC diagnostic ignored "-Wunused-variable"	// not working
#endif

static _E E;

#ifdef __GNUC__
	#pragma GCC diagnostic pop
#endif




// E unused
#ifdef __GNUC__
	template<class T>void ___fhsdhsdhrtsh(){(void)E;}
#endif




#include<cstdlib>






namespace ab
{

	/*
	template<typename Ret, typename T>
	class Binder
	{
	public:
		Binder(Ret T::*_var) : var(_var) {}
		Ret& operator()(T& obj) const
		{
			return obj.*var;
		}
		const Ret& operator()(const T& obj) const
		{
			return obj.*var;
		}
	private:
		Ret T::*var;
	};

	template<typename Ret, typename T>
	Binder<Ret,T> bind(Ret T::*var)
	{
		return Binder<Ret,T>(var);
	}*/
	
	
	
	
	
	/*
	
	template<class A, class B>
	__typeof(A()+B()) plus(const A& a, const B& b){return a+b;}
	
	template<class A, class B>
	__typeof(A()-B()) minus(const A& a, const B& b){return a-b;}
	
	template<class A, class B>
	__typeof(A()*B()) multiplies(const A& a, const B& b){return a*b;}
	
	template<class A, class B>
	__typeof(A()/B()) divides(const A& a, const B& b){return a/b;}
	
	
	
	template<class A, class B>
	A& plus_assign(A& a,const B& b){return a+=b;}
	
	template<class A, class B>
	A& minus_assign(A& a,const B& b){return a-=b;}
	
	template<class A, class B>
	A& multiplies_assign(A& a,const B& b){return a*=b;}
	
	template<class A, class B>
	A& divides_assign(A& a,const B& b){return a/=b;}
	
	*/
	

}






//#include<type_traits>

namespace ab
{


template<bool cond, typename T, typename F> struct IF {typedef T R;};
template<typename T, typename F> struct IF<false,T,F> {typedef F R;};

template <bool B, class T = void> struct ENABLE_IF {typedef T R;};
template <class T> struct ENABLE_IF<false, T> {};

template <bool B, class T = void> struct DISABLE_IF {typedef T R;};
template <class T> struct DISABLE_IF<true, T> {};



template<class A, class B> struct SAME{ static const bool r = false;};
template<typename T> struct SAME<T,T>{	static const bool r = true;};


template<typename T>
struct IS_CLASS{
	template<typename C> static char (&f(int C::*))[1];
	template<typename C> static char (&f(...))[2];

	static bool const r = sizeof(f<T>(0))==sizeof(char);
};




// remove reference
template<class T> struct RR{typedef T R;};
template<class T> struct RR<T&>{typedef T R;};

//remove const
template<class T> struct RC{typedef T R;};
template<class T> struct RC<const T>{typedef T R;};

// remove const and reference
template<class T> struct RRC{typedef typename RC<typename RR<T>::R>::R R;};


#define TYPE(T,...) typename T<__VA_ARGS__>::R





struct TRU{static const bool r = true;  typedef TRU R;};
struct FAL{static const bool r = false; typedef FAL R;};



// SFINAE test
#define HAS_MEMBER(member_alias, member)																									\
template<typename __T> struct HAS_CLASS_##member_alias {																											\
    struct Fallback { void member(); };																											\
    struct Derived : __T, Fallback { };																											\
																											\
    template<typename C, C> struct ChT;																											\
																											\
    template<typename C> static char (&f(ChT<void (Fallback::*)(), &C::member>*))[1];													\
    template<typename C> static char (&f(...))[2];																								\
																											\
    static const bool r = sizeof(f<Derived>(0)) == 2;																						\
};																										\
template<typename __T>																											\
struct HAS_##member_alias																											\
{																											\
	typedef typename IF<IS_CLASS<__T>::r, HAS_CLASS_##member_alias<__T>, FAL>::R R;														\
	static const bool r = R::r;																									\
};






// Dzia│a dok│adnie, uwzglŕdnia typ (const, referencje) wyniku i argumentˇw, uwzglŕdnia const membera
// Przyk│ad dla non-static klasy A:
// typedef int (A::*sign1)(unsigned short&); 
// Przyk│ad dla static dowolnej klasy:
// typedef int (*sign1)(unsigned short&); 
#define HAS_MEMBER_SIG(member_name, member_signature)																			\
template<typename CLS>																							\
struct HAS_SIG_##member_name																															\
{																									\
    template<typename C, C> struct ChT;																													\
	template<typename C> static char (&f(ChT<member_signature, &C::member_name>*))[1];																\
	template<typename C> static char (&f(...))[2];																									\
	static const bool r = sizeof(f<CLS>(0)) == sizeof(char);																							\
};




HAS_MEMBER(OPERATOR_CALL, operator())




/*
// get &T::x or &T::first
template<class T,class=void>struct GET_X{};
template<class T>struct GET_X<T,typename std::enable_if<std::is_object<decltype(T::x)>::value>::type>{typedef decltype(&T::x) R;};
template<class T>struct GET_X<T,typename std::enable_if<std::is_object<decltype(T::first)>::value>::type>{typedef decltype(&T::first) R;};

// get &T::y or &T::second
template<class T,class=void>struct GET_Y{};
template<class T>struct GET_Y<T,typename std::enable_if<std::is_object<decltype(T::y)>::value>::type>{typedef decltype(&T::y) R;};
template<class T>struct GET_Y<T,typename std::enable_if<std::is_object<decltype(T::second)>::value>::type>{typedef decltype(&T::second) R;};
*/

}






#include<utility>

namespace ab{

	struct Identity{
		template<class TT>
		TT operator()(TT&& x)const {
			return std::forward<TT>(x);
		}
		template<class TT>
		TT operator[](TT&& x) const {
			return std::forward<TT>(x);
		}
	};

}




namespace ab{

struct Lambda1{
	template<class A1>
	const A1& operator()(const A1& a1)const{return a1;}
	template<class A1>
	      A1& operator()(      A1& a1)const{return a1;}
	
	template<class A1,class A2>
	const A1& operator()(const A1& a1, const A2&)const{return a1;}
	template<class A1,class A2>
	      A1& operator()(      A1& a1, const A2&)const{return a1;}
	
	template<class A1,class A2,class A3>
	const A1& operator()(const A1& a1, const A2&, const A3&)const{return a1;}
	template<class A1,class A2,class A3>
	      A1& operator()(      A1& a1, const A2&, const A3&)const{return a1;}
};


struct Lambda2{
	template<class A1,class A2>
	const A2& operator()(const A1& a1, const A2& a2)const{return a2;}
	template<class A1,class A2>
	      A2& operator()(const A1& a1,       A2& a2)const{return a2;}
	
	template<class A1,class A2,class A3>
	const A2& operator()(const A1& a1, const A2& a2, const A3& a3)const{return a2;}
	template<class A1,class A2,class A3>
	      A2& operator()(const A1& a1,       A2& a2, const A3& a3)const{return a2;}
};


struct Lambda3{
	template<class A1,class A2,class A3>
	const A3& operator()(const A1& a1, const A2& a2, const A3& a3)const{return a3;}
	template<class A1,class A2,class A3>
	      A3& operator()(const A1& a1, const A2& a2,       A3& a3)const{return a3;}
};


#ifdef __GNUC__
	#pragma GCC diagnostic push
	#pragma GCC diagnostic ignored "-Wunused-variable"	// not working
#endif


static Lambda1 _1;
static Lambda2 _2;
static Lambda3 _3;
//#define _1 Lambda1()
//#define _2 Lambda2()
//#define _3 Lambda3()



#ifdef __GNUC__
#pragma GCC diagnostic pop
#endif




#ifdef __GNUC__
	// _1 _2 _3 unused
	// pragma diagnostic ignored not working?
	template<class T>void ___fhsdhsdhrtshx(){(void)_1;(void)_2;(void)_3;}
#endif







template<class L, class A1, class A2, class A3> struct RET_TYPE3{typedef L& R;};

template<class L, class A1> struct RET_TYPE1{typedef typename RET_TYPE3<L,A1,A1,A1>::R R;};
template<class L, class A1, class A2> struct RET_TYPE2{typedef typename RET_TYPE3<L,A1,A2,A2>::R R;};






// is lambda before evaluation
template<class L> struct IS_LAMBDA{static const bool r = false;};





// is lambda after evaluation
template<class L, class A1, class A2, class A3> struct IS_LAMBDA3{
static const bool r = !SAME<L&, typename RET_TYPE3<L,A1,A2,A3>::R&>::r;};

template<class L, class A1, class A2> struct IS_LAMBDA2{
static const bool r = !SAME<typename RR<L>::R, typename RR<typename RET_TYPE2<L,A1,A2>::R>::R>::r;};

template<class L, class A1> struct IS_LAMBDA1{
static const bool r = !SAME<typename RR<L>::R, typename RR<typename RET_TYPE1<L,A1>::R>::R>::r;};




template<class T, class A1>
typename ENABLE_IF  < IS_LAMBDA1<T,A1>::r,      typename RET_TYPE1<T,const A1>::R>::R Eval(const T& t, const A1& a1){return t(a1);}
template<class T, class A1>
typename ENABLE_IF  < IS_LAMBDA1<T,A1>::r,      typename RET_TYPE1<T,      A1>::R>::R Eval(const T& t,       A1& a1){return t(a1);}

template<class T, class A1>
typename DISABLE_IF < IS_LAMBDA1<T,A1>::r,      typename RET_TYPE1<T,A1>::R&>::R Eval(      T& t, const A1& a1){return t;}




template<class T, class A1, class A2>
typename ENABLE_IF < IS_LAMBDA2<T,A1,A2>::r,      typename RET_TYPE2<T,const A1,const A2>::R>::R Eval(const T& t, const A1& a1, const A2& a2){return t(a1,a2);}
template<class T, class A1, class A2>
typename ENABLE_IF < IS_LAMBDA2<T,A1,A2>::r,      typename RET_TYPE2<T,const A1,      A2>::R>::R Eval(const T& t, const A1& a1,       A2& a2){return t(a1,a2);}
template<class T, class A1, class A2>
typename ENABLE_IF < IS_LAMBDA2<T,A1,A2>::r,      typename RET_TYPE2<T,      A1,const A2>::R>::R Eval(const T& t,       A1& a1, const A2& a2){return t(a1,a2);}
template<class T, class A1, class A2>
typename ENABLE_IF < IS_LAMBDA2<T,A1,A2>::r,      typename RET_TYPE2<T,      A1,      A2>::R>::R Eval(const T& t,       A1& a1,       A2& a2){return t(a1,a2);}

template<class T, class A1, class A2>
typename DISABLE_IF< IS_LAMBDA2<T,A1,A2>::r,      typename RET_TYPE2<T,A1,A2>::R&>::R Eval(      T& t, const A1& a1, const A2& a2){return t;}




template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,const A1,const A2,const A3>::R>::R Eval(const T& t, const A1& a1, const A2& a2, const A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,const A1,const A2,      A3>::R>::R Eval(const T& t, const A1& a1, const A2& a2,       A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,const A1,      A2,const A3>::R>::R Eval(const T& t, const A1& a1,       A2& a2, const A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,const A1,      A2,      A3>::R>::R Eval(const T& t, const A1& a1,       A2& a2,       A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,      A1,const A2,const A3>::R>::R Eval(const T& t,       A1& a1, const A2& a2, const A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,      A1,const A2,      A3>::R>::R Eval(const T& t,       A1& a1, const A2& a2,       A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,      A1,      A2,const A3>::R>::R Eval(const T& t,       A1& a1,       A2& a2, const A3& a3){return t(a1,a2,a3);}
template<class T, class A1, class A2, class A3>
typename ENABLE_IF  < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,      A1,      A2,      A3>::R>::R Eval(const T& t,       A1& a1,       A2& a2,       A3& a3){return t(a1,a2,a3);}

template<class T, class A1, class A2, class A3>
typename DISABLE_IF < IS_LAMBDA3<T,A1,A2,A3>::r,      typename RET_TYPE3<T,A1,A2,A3>::R&>::R Eval(      T& t, const A1& a1, const A2& a2, const A3& a3){return t;}







template<class L1, class L2>
class LambdaPlus{
public:
	LambdaPlus(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaPlus,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) + Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaPlus,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) + Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaPlus,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) + Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};

template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaPlus<L1,L2> >::R operator+(const L1& l1, const L2& l2){
	return LambdaPlus<L1,L2>(l1,l2);
}



template<class L1, class L2>
class LambdaMinus{
public:
	LambdaMinus(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaMinus,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) - Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaMinus,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) - Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaMinus,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) - Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};

template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaMinus<L1,L2> >::R operator-(const L1& l1, const L2& l2){
	return LambdaMinus<L1,L2>(l1,l2);
}






template<class L1>
class LambdaUnaryMinus{
public:
	LambdaUnaryMinus(const L1& _l1) : l1(_l1){}
	
	template<class A1>
	typename RET_TYPE1<LambdaUnaryMinus,A1>::R operator()(const A1& a1)const{
		return -Eval(l1,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaUnaryMinus,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return -Eval(l1,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaUnaryMinus,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return -Eval(l1,a1,a2,a3);
	}
	
private:
	const L1& l1;
};

template<class L1>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r, LambdaUnaryMinus<L1> >::R operator-(const L1& l1){
	return LambdaUnaryMinus<L1>(l1);
}






template<class L1, class L2>
class LambdaMultiplies{
public:
	LambdaMultiplies(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaMultiplies,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) * Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaMultiplies,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) * Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaMultiplies,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) * Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};

template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaMultiplies<L1,L2> >::R operator*(const L1& l1, const L2& l2){
	return LambdaMultiplies<L1,L2>(l1,l2);
}




template<class L1, class L2>
class LambdaDivides{
public:
	LambdaDivides(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaDivides,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) / Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaDivides,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) / Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaDivides,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) / Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};

template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaDivides<L1,L2> >::R operator/(const L1& l1, const L2& l2){
	return LambdaDivides<L1,L2>(l1,l2);
}














template<class L1, class L2>
class LambdaPlusAssign{
public:
	LambdaPlusAssign(L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1> typename RET_TYPE1<LambdaPlusAssign,A1>::R operator()(const A1& a1)const{return Eval(l1,a1) += Eval(l2,a1);}
	template<class A1> typename RET_TYPE1<LambdaPlusAssign,A1>::R operator()(      A1& a1)const{return Eval(l1,a1) += Eval(l2,a1);}
	
	template<class A1, class A2> typename RET_TYPE2<LambdaPlusAssign,const A1,const A2>::R operator()(const A1& a1, const A2& a2)const{return Eval(l1,a1,a2) += Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaPlusAssign,const A1,      A2>::R operator()(const A1& a1,       A2& a2)const{return Eval(l1,a1,a2) += Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaPlusAssign,      A1,const A2>::R operator()(      A1& a1, const A2& a2)const{return Eval(l1,a1,a2) += Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaPlusAssign,      A1,      A2>::R operator()(      A1& a1,       A2& a2)const{return Eval(l1,a1,a2) += Eval(l2,a1,a2);}
	
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(const A1& a1, const A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(const A1& a1,       A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(const A1& a1,       A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(      A1& a1, const A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(      A1& a1, const A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(      A1& a1,       A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaPlusAssign,A1,A2,A3>::R operator()(      A1& a1,       A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3) += Eval(l2,a1,a2,a3);}
	
private:
	L1& l1;
	const L2& l2;
};


template<class L1, class L2>
typename ENABLE_IF<IS_LAMBDA<L1>::r or IS_LAMBDA<L2>::r, LambdaPlusAssign<L1,L2> >::R operator+=(L1& l1, const L2& l2){
	return LambdaPlusAssign<L1,L2>(l1,l2);
}







// LOGICAL

template<class L1, class L2>
class LambdaLess{
public:
	LambdaLess(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaLess,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) < Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaLess,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) < Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaLess,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) < Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};
template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaLess<L1,L2> >::R operator<(const L1& l1, const L2& l2){
	return LambdaLess<L1,L2>(l1,l2);
}





template<class L1, class L2>
class LambdaGreater{
public:
	LambdaGreater(const L1& _l1, const L2& _l2) : l1(_l1), l2(_l2){}
	
	template<class A1>
	typename RET_TYPE1<LambdaGreater,A1>::R operator()(const A1& a1)const{
		return Eval(l1,a1) > Eval(l2,a1);
	}
	
	template<class A1, class A2>
	typename RET_TYPE2<LambdaGreater,A1,A2>::R operator()(const A1& a1, const A2& a2)const{
		return Eval(l1,a1,a2) > Eval(l2,a1,a2);
	}
	
	template<class A1, class A2, class A3>
	typename RET_TYPE3<LambdaGreater,A1,A2,A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{
		return Eval(l1,a1,a2,a3) > Eval(l2,a1,a2,a3);
	}
	
private:
	const L1& l1;
	const L2& l2;
};

template<class L1, class L2>
typename ENABLE_IF<HAS_OPERATOR_CALL<L1>::r or HAS_OPERATOR_CALL<L2>::r, LambdaGreater<L1,L2> >::R operator>(const L1& l1, const L2& l2){
	return LambdaGreater<L1,L2>(l1,l2);
}






template<class L1, class L2>
class LambdaDotStar{
public:
	LambdaDotStar(L1& _l1, const L2& _l2) : l1(_l1), l2(_l2) {}
	
	template<class A1> typename RET_TYPE1<LambdaDotStar,const A1>::R operator()(const A1& a1)const{return Eval(l1,a1).*Eval(l2,a1);}
	template<class A1> typename RET_TYPE1<LambdaDotStar,      A1>::R operator()(      A1& a1)const{return Eval(l1,a1).*Eval(l2,a1);}
	
	template<class A1, class A2> typename RET_TYPE2<LambdaDotStar,const A1,const A2>::R operator()(const A1& a1, const A2& a2)const{return Eval(l1,a1,a2).*Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaDotStar,const A1,      A2>::R operator()(const A1& a1,       A2& a2)const{return Eval(l1,a1,a2).*Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaDotStar,      A1,const A2>::R operator()(      A1& a1, const A2& a2)const{return Eval(l1,a1,a2).*Eval(l2,a1,a2);}
	template<class A1, class A2> typename RET_TYPE2<LambdaDotStar,      A1,      A2>::R operator()(      A1& a1,       A2& a2)const{return Eval(l1,a1,a2).*Eval(l2,a1,a2);}
	
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,const A1,const A2,const A3>::R operator()(const A1& a1, const A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,const A1,const A2,      A3>::R operator()(const A1& a1, const A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,const A1,      A2,const A3>::R operator()(const A1& a1,       A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,const A1,      A2,      A3>::R operator()(const A1& a1,       A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,      A1,const A2,const A3>::R operator()(      A1& a1, const A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,      A1,const A2,      A3>::R operator()(      A1& a1, const A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,      A1,      A2,const A3>::R operator()(      A1& a1,       A2& a2, const A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}
	template<class A1, class A2, class A3> typename RET_TYPE3<LambdaDotStar,      A1,      A2,      A3>::R operator()(      A1& a1,       A2& a2,       A3& a3)const{return Eval(l1,a1,a2,a3).*Eval(l2,a1,a2,a3);}

private:
	L1& l1;
	const L2& l2;
};

// bv == bind var
template<class PTR, class T>
LambdaDotStar<const T,PTR> bv(const PTR& ptr, const T& t){
	return LambdaDotStar<const T,PTR>(t,ptr);
}
template<class PTR, class T>
LambdaDotStar<T,PTR> bv(const PTR& ptr, T& t){
	return LambdaDotStar<T,PTR>(t,ptr);
}








// is lambda (before evaluation)
template<> struct IS_LAMBDA<Lambda1>{static const bool r = true;};
template<> struct IS_LAMBDA<Lambda2>{static const bool r = true;};
template<> struct IS_LAMBDA<Lambda3>{static const bool r = true;};
template<class A,class B> struct IS_LAMBDA<LambdaPlus<A,B> >{static const bool r = true;};
template<class A,class B> struct IS_LAMBDA<LambdaMinus<A,B> >{static const bool r = true;};
template<class A,class B> struct IS_LAMBDA<LambdaMultiplies<A,B> >{static const bool r = true;};
template<class A,class B> struct IS_LAMBDA<LambdaDivides<A,B> >{static const bool r = true;};
template<class A,class B> struct IS_LAMBDA<LambdaPlusAssign<A,B> >{static const bool r = true;};
// TODO
















// lambda return types

/*
template<class A1> struct RET_TYPE1<Lambda1,A1>{typedef A1 R;};

template<class A1, class A2> struct RET_TYPE2<Lambda1,A1,A2>{typedef A1 R;};
template<class A1, class A2> struct RET_TYPE2<Lambda2,A1,A2>{typedef A2 R;};
*/
template<class A1, class A2, class A3> struct RET_TYPE3<Lambda1,A1,A2,A3>{typedef A1& R;};
template<class A1, class A2, class A3> struct RET_TYPE3<Lambda2,A1,A2,A3>{typedef A2& R;};
template<class A1, class A2, class A3> struct RET_TYPE3<Lambda3,A1,A2,A3>{typedef A3& R;};




#ifdef _MSC_VER
	#define __typeof decltype
#endif



template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaPlus<L1,L2>,A1,A2,A3>{
	typedef __typeof(TYPE(RRC,typename RET_TYPE3<L1,A1,A2,A3>::R)() + TYPE(RRC,typename RET_TYPE3<L2,A1,A2,A3>::R)()) R;
};

template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaMinus<L1,L2>,A1,A2,A3>{
	typedef __typeof(TYPE(RRC,typename RET_TYPE3<L1,A1,A2,A3>::R)() - TYPE(RRC,typename RET_TYPE3<L2,A1,A2,A3>::R)()) R;
};

template<class L1, class A1, class A2, class A3> struct RET_TYPE3<LambdaUnaryMinus<L1>,A1,A2,A3>{
	typedef __typeof(- TYPE(RRC,typename RET_TYPE3<L1,A1,A2,A3>::R)()) R;
};

template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaMultiplies<L1,L2>,A1,A2,A3>{
	typedef __typeof(*(typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R*)nullptr * *(typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R*)nullptr) R;
};

template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaDivides<L1,L2>,A1,A2,A3>{
	typedef __typeof(typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R() / typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R()) R;
};



template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaPlusAssign<L1,L2>,A1,A2,A3>{
	typedef __typeof(*(new typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R) += *(new typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R))& R;
};




template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaLess<L1,L2>,A1,A2,A3>{
	typedef __typeof(*(new typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R) < *(new typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R)) R;
};
template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaGreater<L1,L2>,A1,A2,A3>{
	typedef __typeof(*(new typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R) > *(new typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R)) R;
};



template<class L1, class L2, class A1, class A2, class A3> struct RET_TYPE3<LambdaDotStar<L1,L2>,A1,A2,A3>{
	typedef __typeof(*(new typename RRC<typename RET_TYPE3<L1,A1,A2,A3>::R>::R) .* *(new typename RRC<typename RET_TYPE3<L2,A1,A2,A3>::R>::R)) R;
};






template<class F, class L1>
class LambdaBinder1{
public:
	LambdaBinder1(const F& _f, const L1& _l1) : f(_f), l1(_l1) {}
	
	template<class A1>
	int operator()(const A1& a1){
		return f(Eval(l1,a1));
	}
	template<class A1, class A2>
	int operator()(const A1& a1, const A2& a2){
		return f(Eval(l1,a1,a2));
	}
	template<class A1, class A2, class A3>
	int operator()(const A1& a1, const A2& a2, const A3& a3){
		return f(Eval(l1,a1,a2,a3));
	}
	
private:
	const F& f;
	const L1& l1;
};

template<typename F, class L1>
LambdaBinder1<F,L1> bf(const F& f, const L1& l1){
	return LambdaBinder1<F,L1>(f,l1);
}



template<class F, class L1, class L2>
class LambdaBinder2{
public:
	LambdaBinder2(const F& _f, const L1& _l1, const L2& _l2) : f(_f), l1(_l1), l2(_l2) {}
	
	template<class A1>
	int operator()(const A1& a1){
		return f(Eval(l1,a1),Eval(l2,a1));
	}
	template<class A1, class A2>
	int operator()(const A1& a1, const A2& a2){
		return f(Eval(l1,a1,a2),Eval(l2,a1,a2));
	}
	template<class A1, class A2, class A3>
	int operator()(const A1& a1, const A2& a2, const A3& a3){
		return f(Eval(l1,a1,a2,a3),Eval(l2,a1,a2,a3));
	}
	
private:
	const F& f;
	const L1& l1;
	const L2& l2;
};

template<typename F, class L1, class L2>
LambdaBinder2<F,L1,L2> bf(const F& f, const L1& l1, const L2& l2){
	return LambdaBinder2<F,L1,L2>(f,l1,l2);
}



template<class F, class L1, class L2, class L3>
class LambdaBinder3{
public:
	LambdaBinder3(const F& _f, const L1& _l1, const L2& _l2, const L3& _l3) : f(_f), l1(_l1), l2(_l2), l3(_l3) {}
	
	template<class A1>
	int operator()(const A1& a1){
		return f(Eval(l1,a1),Eval(l2,a1),Eval(l3,a1));
	}
	template<class A1, class A2>
	int operator()(const A1& a1, const A2& a2){
		return f(Eval(l1,a1,a2),Eval(l2,a1,a2),Eval(l3,a1,a2));
	}
	template<class A1, class A2, class A3>
	int operator()(const A1& a1, const A2& a2, const A3& a3){
		return f(Eval(l1,a1,a2,a3),Eval(l2,a1,a2,a3),Eval(l3,a1,a2,a3));
	}
	
private:
	const F& f;
	const L1& l1;
	const L2& l2;
	const L3& l3;
};

template<typename F, class L1, class L2, class L3>
LambdaBinder3<F,L1,L2,L3> bf(const F& f, const L1& l1, const L2& l2, const L3& l3){
	return LambdaBinder3<F,L1,L2,L3>(f,l1,l2,l3);
}












}




namespace ab
{


// type-less!
#define PI 3.141592653589793238462643383279502884197169399375105820974944


template<typename T, typename IDX=int>
struct binomial
{
	binomial() : n(0), k(0), val(1) {}
	binomial(const IDX& nn, const IDX& kk) : n(nn), val(1){
		ASS(0<=kk);
		if(2*kk<nn){
			k = 0;
			while(k<kk)moveR();
		}
		else{
			k=nn;
			while(k>kk)moveL();
		}
	}
	IDX n,k;
	T val;
	
	operator T(){
		return val;
	}

	bool outside(){
		bool ret = n<0 || k<0 || k>n;
		if(ret)val=0;
		return ret;
	}

	void moveL(){
		--k;
		if(outside()) return;

		if(k==n) val=1;
		else
		{
			val*=(k+1);
			val/=(n-k);
		}
	}
	void moveR(){
		++k;
		if(outside()) return;

		if(k==0) val=1;
		else
		{
			val*=(n-k+1);
			val/=(k);
		}
	}
	void moveD(){
		++n;
		if(outside()) return;

		if(n==k) val=1;
		else
		{
			val*=n;
			val/=(n-k);
		}
	}
	void moveU(){
		--n;
		if(outside()) return;

		val*=(n-k+1);
		val/=(n+1);
	}
};



// GCD
#define gcd __gcd
/*
template<typename T>
T gcd(T a, T b)
{
	while(b!=0)
	{
		T t = a;
		a = a%b;
		b = t;
	}
	return a;
}
*/


// a*aa + b*bb == gcd(a,b)
template<typename T>
T gcdExt(T a, T b, T& aaa, T& bbb)
{
	T a0 = a;
	T b0 = b;

	T aa = 0;
	T bb = 1;
	aaa = 1;
	bbb = 0;
	// niezmiennik: a0*aa  + b0*bb  == b
	// niezmiennik: a0*aaa + b0*bbb == a
	while(b != 0)
	{
		T q = a/b;
		a = a%b;
		// a -= b*(a/b)
		aaa -= aa*q;
		bbb -= bb*q;
		swap(a,b);
		swap(aa,aaa);
		swap(bb,bbb);
	}

	ASS(a0*aaa + b0*bbb == a);

	return a;
}



template<class T, class E, class OP>
inline T fpow(T a, E exp, const OP& op, const T& neutral = 1){
	T r = neutral;
	while(exp){
		if(exp&1){
			r = op(r,a);
			--exp;
		}
		else{
			exp >>= 1;
			a = op(a,a);
		}
	}
	return r;
}

template<class T, class E>
inline T fpow(T a, E exp){
	return fpow(a, exp, _1 * _2);
}



template<class T> const T& max2(const T& a, const T& b){return a<b?b:a;}
template<class T> const T& min2(const T& a, const T& b){return b<a?b:a;}




template<class T, class F>
inline T lerp(const T& a, const T& b, const F& alpha){
	return (1.0f-alpha)*a + alpha*b;
}





}



namespace ab{

template<int mod1 = (1u<<31)-1, int mod2 = (1u<<31)-19>
struct H2{
	H2() : h1(0), h2(0) {}
	H2(int x) : h1(x%mod1), h2(x%mod2) {}
	ui32 h1,h2;
	H2& operator+=(const H2& o){
		h1 = (h1+o.h1)%mod1;
		h2 = (h2+o.h2)%mod2;
		return *this;
	}
	H2 operator+(const H2& o)const{
		return H2(*this)+=o;
	}
	H2& operator-=(const H2& o){
		h1 = (mod1+h1-o.h1)%mod1;
		h2 = (mod2+h2-o.h2)%mod2;
		return *this;
	}
	H2 operator-(const H2& o)const{
		return H2(*this)-=o;
	}
	H2& operator*=(const H2& o){
		h1 = (1ULL*h1*o.h1)%mod1;
		h2 = (1ULL*h2*o.h2)%mod2;
		return *this;
	}
	H2 operator*(const H2& o)const{
		return H2(*this)*=o;
	}

	bool operator==(const H2& o)const{
		return h1==o.h1 and h2==o.h2;
	}

	bool operator!=(const H2& o)const{
		return !operator==(o);
	}
};

template<int mod1 = (1u<<31)-1>
struct H1{
	H1() : h1(0) {}
	H1(int x) : h1(x%mod1) {}
	ui32 h1;
	H1& operator+=(const H1& o){
		h1 = (h1+o.h1);
		if(h1>=mod1)h1-=mod1;
		return *this;
	}
	H1 operator+(const H1& o)const{
		return H1(*this)+=o;
	}
	H1& operator-=(const H1& o){
		h1 = (mod1+h1-o.h1);
		if(h1>=mod1)h1-=mod1;
		return *this;
	}
	H1 operator-(const H1& o)const{
		return H1(*this)-=o;
	}
	H1& operator*=(const H1& o){
		h1 = (1ULL*h1*o.h1)%mod1;
		return *this;
	}
	H1 operator*(const H1& o)const{
		return H1(*this)*=o;
	}
	H1& operator/=(const H1& o){
		//ASS(millerRabin(mod1));
		return (*this)*=fpow(o, mod1-2, _1 * _2, H1(1));
	}
	H1 operator/(const H1& o)const{
		return H1(*this)/=o;
	}

	/*
	bool operator==(const H1& o)const{
		return h1==o.h1;
	}

	bool operator!=(const H1& o)const{
		return !operator==(o);
	}*/

	operator ui32()const{
		return h1;
	}
};





// hash long long,
// fpow multiplication
template<ull mod = (1ULL<<63)-25> // big prime less than (2^64)/2
struct HLL{
	HLL() : h(0) {}
	HLL(ull x) : h(x%mod) {}
	ull h;
	HLL& operator+=(const HLL& o){
		h = (h+o.h);
		if(h>=mod)h-=mod;
		return *this;
	}
	HLL operator+(const HLL& o)const{
		return HLL(*this)+=o;
	}
	HLL& operator-=(const HLL& o){
		h = (mod+h-o.h);
		if(h>=mod)h-=mod;
		return *this;
	}
	HLL operator-(const HLL& o)const{
		return HLL(*this)-=o;
	}
	// multiplication by fast exponentation
	HLL operator*(const HLL& o)const{
		return fpow(*this, (ull)o, _1 + _2, HLL(0));
	}
	HLL& operator*=(const HLL& o){
		*this = *this * o;
		return *this;
	}
	HLL& operator/=(const HLL& o){
		//ASS(millerRabin(mod));
		return (*this)*=fpow(o, mod-2, _1 * _2, HLL(1));
	}
	HLL operator/(const HLL& o)const{
		return HLL(*this)/=o;
	}
	
	HLL& operator--(){
		if(h==0)h=mod-1;
		else --h;
	}
	HLL& operator++(){
		if(h==mod-1)h=0;
		else ++h;
	}

	/*
	bool operator==(const H1& o)const{
		return h1==o.h1;
	}

	bool operator!=(const H1& o)const{
		return !operator==(o);
	}*/

	operator ull()const{
		return h;
	}
};






// 2 ints + 1 long long
template<int mod1 = (1u<<31)-1, int mod2 = (1u<<31)-19>
struct SuperHash2{
	SuperHash2() : h1(0), h2(0), h(0) {}
	SuperHash2(int x) : h1(x%mod1), h2(x%mod2), h(x) {}
	ui32 h1,h2;
	ull h;
	SuperHash2& operator+=(const SuperHash2& o){
		h1 += o.h1;
		h2 += o.h2;
		if(h1>=mod1) h1-=mod1;
		if(h2>=mod2) h2-=mod2;
		h += o.h;
		return *this;
	}
	SuperHash2 operator+(const SuperHash2& o)const{
		return SuperHash2(*this)+=o;
	}
	SuperHash2& operator-=(const SuperHash2& o){
		h1 += mod1-o.h1;
		h2 += mod2-o.h2;
		if(h1>=mod1) h1-=mod1;
		if(h2>=mod2) h2-=mod2;
		h -= o.h;
		return *this;
	}
	SuperHash2 operator-(const SuperHash2& o)const{
		return SuperHash2(*this)-=o;
	}
	SuperHash2& operator*=(const SuperHash2& o){
		h1 = (1ULL*h1*o.h1)%mod1;
		h2 = (1ULL*h2*o.h2)%mod2;
		h *= o.h;
		return *this;
	}
	SuperHash2 operator*(const SuperHash2& o)const{
		return SuperHash2(*this)*=o;
	}

	bool operator==(const SuperHash2& o)const{
		return h1==o.h1 and h2==o.h2 and h==o.h;
	}

	bool operator!=(const SuperHash2& o)const{
		return !operator==(o);
	}
};








// 3 ints + 1 long long
template<int mod1 = (1u<<31)-1, int mod2 = (1u<<31)-19, int mod3 = (1u<<31)-69>
struct SuperHash3{
	SuperHash3() : h1(0), h2(0), h3(0), h(0) {}
	SuperHash3(int x) : h1(x%mod1), h2(x%mod2), h3(x%mod3), h(x) {}
	ui32 h1,h2,h3;
	ull h;
	SuperHash3& operator+=(const SuperHash3& o){
		h1 += o.h1;
		h2 += o.h2;
		h3 += o.h3;
		if(h1>=mod1) h1-=mod1;
		if(h2>=mod2) h2-=mod2;
		if(h3>=mod3) h3-=mod3;
		h += o.h;
		return *this;
	}
	SuperHash3 operator+(const SuperHash3& o)const{
		return SuperHash3(*this)+=o;
	}
	SuperHash3& operator-=(const SuperHash3& o){
		h1 += mod1-o.h1;
		h2 += mod2-o.h2;
		h3 += mod3-o.h3;
		if(h1>=mod1) h1-=mod1;
		if(h2>=mod2) h2-=mod2;
		if(h3>=mod3) h3-=mod3;
		h -= o.h;
		return *this;
	}
	SuperHash3 operator-(const SuperHash3& o)const{
		return SuperHash3(*this)-=o;
	}
	SuperHash3& operator*=(const SuperHash3& o){
		h1 = (1ULL*h1*o.h1)%mod1;
		h2 = (1ULL*h2*o.h2)%mod2;
		h3 = (1ULL*h3*o.h3)%mod3;
		h *= o.h;
		return *this;
	}
	SuperHash3 operator*(const SuperHash3& o)const{
		return SuperHash3(*this)*=o;
	}

	bool operator==(const SuperHash3& o)const{
		return h1==o.h1 and h2==o.h2 and h3==o.h3 and h==o.h;
	}

	bool operator!=(const SuperHash3& o)const{
		return !operator==(o);
	}
};










// dynamic hash
struct H1X{
	H1X(int mod) : mod1(mod), h1(0) {}
	H1X(int mod, int x) : mod1(mod), h1(x%mod1) {}
	//H1X(const H1X& o) : mod1(o.mod1), h1(o.h1) {}
	H1X& operator=(const H1X& o){
		ASS(mod1==o.mod1);
		//mod1 = o.mod1;
		h1 = o.h1;
		return *this;
	}
	const int mod1;
	ui32 h1;
	H1X& operator+=(const H1X& o){
		ASS(mod1==o.mod1);
		h1 = (h1+o.h1)%mod1;
		return *this;
	}
	H1X operator+(const H1X& o)const{
		return H1X(*this)+=o;
	}
	H1X& operator-=(const H1X& o){
		ASS(mod1==o.mod1);
		h1 = (mod1+h1-o.h1)%mod1;
		return *this;
	}
	H1X operator-(const H1X& o)const{
		return H1X(*this)-=o;
	}
	H1X& operator*=(const H1X& o){
		ASS(mod1==o.mod1);
		h1 = (1ULL*h1*o.h1)%mod1;
		return *this;
	}
	H1X operator*(const H1X& o)const{
		return H1X(*this)*=o;
	}
	H1X& operator/=(const H1X& o){
		ASS(mod1==o.mod1);
		//ASS(millerRabin(mod1));
		return (*this)*=fpow(o,mod1-2, (_1 * _2), H1X(mod1,1));
	}
	H1X operator/(const H1X& o)const{
		return H1X(*this)/=o;
	}

	/*
	bool operator==(const H1X& o)const{
		return h1==o.h1;
	}

	bool operator!=(const H1X& o)const{
		return !operator==(o);
	}*/

	operator ui32()const{
		return h1;
	}

	template<class T>
	explicit operator T()const{
		return h1;
	}
};


template<class INT> H1X operator/(const H1X& h, const INT& i){ ASS(h.mod1);
	return h / H1X(h.mod1,i);
}
template<class INT> H1X operator/(const INT& i, const H1X& h){ ASS(h.mod1);
	return H1X(h.mod1,i) / h;
}

template<class INT> H1X operator*(const H1X& h, const INT& i){ ASS(h.mod1);
	return h * H1X(h.mod1,i);
}
template<class INT> H1X operator*(const INT& i, const H1X& h){ ASS(h.mod1);
	return H1X(h.mod1,i) * h;
}

template<class INT> H1X operator+(const H1X& h, const INT& i){ ASS(h.mod1);
	return h + H1X(h.mod1,i);
}
template<class INT> H1X operator+(const INT& i, const H1X& h){ ASS(h.mod1);
	return H1X(h.mod1,i) + h;
}

template<class INT> H1X operator-(const H1X& h, const INT& i){ ASS(h.mod1);
	return h - H1X(h.mod1,i);
}
template<class INT> H1X operator-(const INT& i, const H1X& h){ ASS(h.mod1);
	return H1X(h.mod1,i) - h;
}



}



#if __cplusplus >= 201103L or defined _MSC_VER
#include <unordered_map>
namespace std{
#else
#include <ext/hash_map>
namespace __gnu_cxx{
#endif

template<int h1, int h2> struct hash<ab::H2<h1,h2> >{
	size_t operator()(const ab::H2<h1,h2>& h)const{
		return h.h1^h.h2;
	}
};
template<int h1> struct hash<ab::H1<h1> >{
	size_t operator()(const ab::H1<h1>& h)const{
		return h.h1;
	}
};

}



















////////////////////////////////////////////////////////////////////////////////
//                                                                            //
//  ACTUAL SOLUTION IS AT THE END OF THIS FILE!!!                             //
//                                                                            //
////////////////////////////////////////////////////////////////////////////////


















////////////////////////// PROTOTYPING TEMPLATE /////////////////////////////////
//
// Implementation: Adam Blaszkiewicz (atablash.pl), 2012-2014
/*
    This program is licensed under GNU General Public License version 3.
    See <http://www.gnu.org/licenses/>.
*/
//
//

// enable c++ iostream; only if no fastio
//#define IOSTREAM

//#define NO_UNLOCKED	// fread_unlocked, fwrite_unlocked



// PRIi64, PRIui64
#define __STDC_FORMAT_MACROS
#include<inttypes.h>



//#if MIN_GCC(4,1,3)
//#include<bits/stdc++.h>
//#else
#include<vector>
#include<map>
#include<queue>
#include<algorithm>
#include<string>
#include<stdint.h>
#include<cstring>
#include<iostream>
#include<set>
#include<climits>
#include<bitset>
#include<limits>
#include<sstream>
#include<cmath>
//#endif








/*
#define fo3(i,a,b) for(int i=(int)(a); i<(int)(b); ++i)
#define of3(i,a,b) for(int i=(int)((b)-1); i>=(int)(a); --i)

#define fo2(i,n) fo3(i,0,n)
#define of2(i,n) of3(i,0,n)

#define fo(...) VA_SEL(fo,__VA_ARGS__)
#define of(...) VA_SEL(of,__VA_ARGS__)
*/

#define inl		inline __attribute__ ((always_inline))
#define ninl	__attribute__ ((noinline))







#ifdef DEBUG_BUILD
	#undef FASTIO
#endif





#ifdef _WIN32

// TODO
#ifndef NO_UNLOCKED
#define NO_UNLOCKED
#endif

//#define fread_unlocked _fread_nolock
//#define fwrite_unlocked _fwrite_nolock

#endif



using namespace std;
using namespace __gnu_cxx;

namespace ab{}
using namespace ab;





template<class T>inline void sortu(T& t){t.resize(std::unique(ALL(t))-t.be);}


inline uint _rand(){
	if(RAND_MAX < (1<<15)) return (rand()<<15) | rand();
	else return rand();
}
#define RND _rand()


#define ri _rint()
#define rui _ruint()
#define rll _rll()
#define rull _rull()
#define rchar _rchar()
#define rstr _rstr()


#ifndef FASTIO
inline void _fin(int){}
inline void _fout(int){}
#ifdef IOSTREAM
inline int _rint(){int r;cin>>r;return r;}
inline uint _ruint(){uint r;cin>>r;return r;}
inline ull _rull(){ull r;cin>>r;return r;}
inline ll _rll(){ll r;cin>>r;return r;}
inline char _rchar(){return cin.get();}
inline string _rstr(){string s;cin>>s;return s;}
template<typename T>inline void W(const T& i){cout<<i; cout.flush();}
inline void W(){W('\n');}
#else
inline int _rint(){int r;scanf("%d",&r);return r;}
inline uint _ruint(){uint r;scanf("%u",&r);return r;}
inline ull _rull(){ull r;scanf("%" SCNu64,&r);return r;}
inline ull _rll(){ll r;scanf("%" SCNd64,&r);return r;}
inline char _rchar(){return getchar();}
inline string _rstr(){
	string s;
	char c=rchar;
	while(c!=-1 && !isgraph(c))c=rchar;
	for(;;){
		if(!isgraph(c))break;
		s+=c;
		c=rchar;
	}
	return s;
}
inline void W(char a='\n'){printf("%c",a);}
inline void W(const string&s){printf("%s",s.c_str());}
inline void W(int a){printf("%d",a);}
inline void W(uint a){printf("%u",a);}
inline void W(const ui64& a){printf("%" PRIu64,a);}
inline void W(const i64& a){printf("%" PRIi64,a);}
inline void W(const char *str){fputs(str,stdout);}
inline void W(const double& d){printf("%.20f",d);}
inline void W(const long double& d){printf("%.50Lf",d);}
#endif
#else

#ifndef NO_UNLOCKED
#define FREAD fread_unlocked
#define FWRITE fwrite_unlocked
#else
#define FREAD fread
#define FWRITE fwrite
#endif

// todo: test on pointers
const int _IB=32768;const int _OB=32768;
char _iB[_IB];int _iP = _IB;
char _oB[_OB];int _oP = 0;
inline void _fin(int mc){
	int r=_IB-_iP;
	if(r>mc)return;
	FOR(i,r) _iB[i]=_iB[i+_iP];	// TODO: try memcpy
    int rd=FREAD(_iB+r,1,_iP,stdin);
	if(rd!=_iP) _iB[r+rd]=0;
	_iP = 0;
}
inline void _fout(int mc){
	if(_OB-_oP>mc)return;
	FWRITE(_oB,1,_oP,stdout);
	_oP = 0;
}
inline void _W(char c='\n'){_oB[_oP++]=c;} // unchecked!
inline char _rc(){return _iB[_iP++];}
inline char _rchar(){_fin(1);return _rc();}
inline string _rstr(){
	string s;
	for(;;){
		char c=rchar;
		if(!isprint(c)||isspace(c))break;
		s+=c;
	}
	return s;
}
template<class T>inline T _rur(){ // unchecked!
    T r=0;char c=_rc();
    do c-='0',r=r*10+c,c=_rc();while(c>='0');
    return r;}
template<class T>inline T _rsi(){ // unchecked!
	char c=_rc();
	while(c<'-')c=_rc();
	if(c=='-')return -_rur<T>();
	else{--_iP;return _rur<T>();}}
template<class T>inline T _ru(){  // unchecked!
	while(_rc()<'0');--_iP;
	return _rur<T>();
}

inline int _rint(){_fin(15);return _rsi<int>();}
inline uint _ruint(){_fin(15);return _ru<uint>();}
inline ll _rll(){_fin(25);return _rsi<ll>();}
inline ull _rull(){_fin(25);return _ru<ull>();}

const int _rs = 20; char _r[_rs];
template<class T>inline void _w(T i){	// unchecked!
	if(numeric_limits<T>::is_signed and i<0) _W('-'), i=-i;
	else if(i==0){_W('0'); return;}
	int pos = _rs;
	do _r[--pos]='0'+i%10, i/=10; while(i);
	do _W(_r[pos++]); while(pos<_rs);
}
inline void W(const char c){_fout(2);_W(c);}
inline void W(const int32_t& i){_fout(15);_w(i);}
inline void W(const uint32_t& i){_fout(15);_w(i);}
inline void W(const int64_t& i){_fout(25);_w(i);}
inline void W(const uint64_t& i){_fout(25);_w(i);}
inline void W(const char*str, int l){
	for(int b=0; b<l; b+=_OB){
		int num = min(_OB,l-b);
		_fout(num);
		memcpy(&_oB[_oP], str+b, num);
		_oP+=num;
	}
}
inline void W(const char*str){W(str,strlen(str));}
inline void W(const string&s){W(s.c_str(),s.siz);}
inline void W(double d){_fout(50);_oP+=sprintf(&_oB[_oP],"%.20f",d);}	// todo
#endif
template<class A,class B>inline void W(const A&a,const B&b){W(a);W(b);}
template<class A,class B,class C>
inline void W(const A&a,const B&b,const C&c){W(a);W(b);W(c);}
template<class A,class B,class C,class DD>
inline void W(const A&a,const B&b,const C&c,const DD&dd){W(a);W(b);W(c);W(dd);}
template<class T>inline void sortall(T&t){sort(t.be,t.en);}
template<class T>inline void uniqall(T&t){t.resize(unique(t.be,t.en)-t.be);}


#define rgraph _rgraph()
inline char _rgraph(){char c;do c=rchar;while(!isgraph(c));return c;}

#define subset(a,b) (a&b==a)
#define kbegin(k) ((1<<k)-1)
#define kend(k,n) ((kbegin(k)<<n-k)+1)
inline uint knext(uint a){uint b=(a|(a-1))+1;return b|((a^b)>>(__builtin_ctz(a)+2));}
#define fors(x,k,n) for(uint x=kbegin(k);x<kend(k,n);x=knext(x))

struct _O{template<class T>_O&operator<(const T&_t){
		oc(1);W(_t);oc(0);
		return *this;
}}O;

struct _I{
	_I&operator>(int32_t&_t){_t=ri;return*this;}
	_I&operator>(uint32_t&_t){_t=rui;return*this;}
	_I&operator>(int64_t&_t){_t=rll;return*this;}
	_I&operator>(uint64_t&_t){_t=rull;return*this;}
	_I&operator>(char&_t){_t=rchar;return*this;}
	_I&operator>(string&_t){_t=rstr;return*this;}
}I;




inline void tc();
#ifdef GEN
int argc;  char **argv;
int main(int _argc, char *_argv[]){
	argc = _argc;  argv = _argv;
	if(argc<2){
		O < "Usage: " < argv[0] < " NR_TESTU" < N;
		return 1;
	}
	srand(atoi(argv[1]));
#else
int main(){
#endif

	//Log log;
	//log.autoFlush = true;
	//Log::global() = &log;

#ifdef FASTIO
    setvbuf(stdin,0,_IONBF,0);setvbuf(stdout,0,_IONBF,0);
#elif defined IOSTREAM
	ios_base::sync_with_stdio(0);cout.precision(10);cout.setf(ios::fixed,ios::floatfield);
	#if not defined DEBUG_BUILD and not defined COLOR_CONSOLE
	cin.tie(0);
	#endif
#endif

#ifdef DEBUG_BUILD
#ifdef _WIN32
	ec(0);
	oc(0);
#else
// TODO: *nix
#endif
#endif
	
#ifdef READ_NUM_TEST_CASES
	int nz=rui;FOR(i,nz)
#endif
	tc();
#ifdef FASTIO
    FWRITE(_oB,1,_oP,stdout);
#endif
	return 0;
}
// END OF TEMPLATE





































////////////////////////////////////////////////////////////////////////////////
//                                                                            //
//  ACTUAL SOLUTION BEGINS HERE:                                              //
//                                                                            //
////////////////////////////////////////////////////////////////////////////////

#include "poszukiwania.h"
#include "message.h"





typedef SuperHash3<> H;
//typedef SuperHash2<> H;
//typedef H2<> H;

// meta
int numberOfNodes;
int myNodeId;

// input
int textSize;
int pattSize;


// common
const int base = 1000000117;

int numPrzylozenia;
int przylozeniaPerNode;

H patternHash;

inline int seqAt(int i){
	return SeqAt(i+1)+1;
}

inline int signalAt(int i){
	return SignalAt(i+1)+1;
}


const int maxMessageSize = 256 * 1024;

const int hashSize = 3*4 + 8; // !!!
inline void putHash(int target, const H& value){
	PutInt(target, value.h1);
	PutInt(target, value.h2);
	PutInt(target, value.h3);
	PutLL(target, value.h);
}

inline H getHash(int from){
	H h;
	h.h1 = GetInt(from);
	h.h2 = GetInt(from);
	h.h3 = GetInt(from);
	h.h = GetLL(from);
	return h;
}


// instance 0
int numTextPrefsumBlocks;
int textPrefsumBlockSize;
int blocksPerNode;
vector<H> textPrefsumSparse;
//ull textPrefsumSparse2[1010000000 / textPrefsumBlockSize];


// worker


inline pii getPrefsumFragmentBounds(int iBlock){
	int fr = iBlock*textPrefsumBlockSize;
	int to = (iBlock+1)*textPrefsumBlockSize;
	if(to >= textSize) to = textSize;
	if(fr>to) fr = to;
	return mp(fr,to);
}

void workerComputePrefsumFragment(){
	textPrefsumBlockSize = sqrt(textSize);
	if(textPrefsumBlockSize <= 0) textPrefsumBlockSize = 1;
	numTextPrefsumBlocks = (textSize + textPrefsumBlockSize - 1) / textPrefsumBlockSize;
	
	if(myNodeId==0) E < "prefsum block size: " < textPrefsumBlockSize < NL;
	
	
	blocksPerNode = (numTextPrefsumBlocks + numberOfNodes - 1) / numberOfNodes;
	
	int messageSize = 0;
	
	FOR(i,blocksPerNode){
		int iBlock = blocksPerNode*myNodeId + i;
		pii bounds = getPrefsumFragmentBounds(iBlock);
		if(bounds.fi == bounds.se) break;
		
		H cHash = 0;
		H basePow = fpow((H)base, bounds.fi);
		FO(j, bounds.fi, bounds.se){
			cHash += basePow * seqAt(j);
			basePow *= base;
		}
		E < "computed hash " < cHash.h1 < " for block " < iBlock < NL;
		
		if(messageSize + hashSize > maxMessageSize){
			Send(0);
			messageSize = 0;
		}
		putHash(0,cHash);
		messageSize += hashSize;
	}
	Send(0);
}


void masterSendPrefsums(){
	if(myNodeId != 0) return;
	
	textPrefsumSparse.resize(numTextPrefsumBlocks+1);
	
	// receive prefsum fragments
	//FOR(kk,numberOfNodes){
		//int fromNode = Receive(-1);
	FOR(fromNode,numberOfNodes){
		Receive(fromNode);
		int messageSize = 0;
		
		FOR(i,blocksPerNode){
			int iBlock = blocksPerNode*fromNode + i;
			pii bounds = getPrefsumFragmentBounds(iBlock);
			if(bounds.fi == bounds.se) break;
			
			if(messageSize + hashSize > maxMessageSize){
				Receive(fromNode);
				messageSize = 0;
			}
			
			H h = getHash(fromNode);
			messageSize += hashSize;
			textPrefsumSparse[iBlock+1] = h;
		}
	}
	FOR(i,numTextPrefsumBlocks) textPrefsumSparse[i+1] += textPrefsumSparse[i];
	
	// send required prefsums
	FOR(iNode,numberOfNodes){
		int przylozenie = przylozeniaPerNode*iNode;
		int fullBlocks = przylozenie / textPrefsumBlockSize;
		int fullBlocks2 = (przylozenie + pattSize) / textPrefsumBlockSize;
		putHash(iNode, textPrefsumSparse[fullBlocks]);
		putHash(iNode, textPrefsumSparse[fullBlocks2]);
		Send(iNode);
	}
}


inline void tc(){
	numberOfNodes = NumberOfNodes();
	myNodeId = MyNodeId();
	
	textSize = SeqLength();
	pattSize = SignalLength();
	
	numPrzylozenia = textSize-pattSize+1;
	przylozeniaPerNode = (numPrzylozenia+numberOfNodes-1) / numberOfNodes;
	
	// compute prefsums
	workerComputePrefsumFragment();
	masterSendPrefsums();
	
	if(myNodeId==0) E < "prefsums computed" < NL;
	
	// compute pattern hash
	patternHash = 0;
	OF(i,0,pattSize){
		patternHash *= base;
		patternHash += signalAt(i);
	}
	
	if(myNodeId==0) E < "pattern hash computed. " < patternHash.h1 < NL;
	
	int fr = myNodeId*przylozeniaPerNode;
	int to = fr + przylozeniaPerNode;
	
	Receive(0);
	H prefsumLeft = getHash(0);
	H prefsumRight = getHash(0);
	
	//if(myNodeId==0) cerr << "prefsums sent" << endl;
	
	int iLeft = fr / textPrefsumBlockSize * textPrefsumBlockSize;
	H basePowLeft = fpow((H)base,iLeft);
	FO(i, iLeft, fr){
		prefsumLeft += basePowLeft * seqAt(i);
		basePowLeft *= base;
	}
	
	int iRight = (fr + pattSize) / textPrefsumBlockSize * textPrefsumBlockSize;
	H basePowRight = fpow((H)base,iRight);
	FO(i, iRight, fr + pattSize){
		prefsumRight += basePowRight * seqAt(i);
		basePowRight *= base;
	}
	
	patternHash *= fpow((H)base, fr);
	
	int result = 0;
	
	FO(i, fr, to){
		if(i >= numPrzylozenia)break;
		
		// check przylozenie 'i'
		H candHash = prefsumRight - prefsumLeft;
		E < "position " < i < ":  candHash==" < candHash.h1
			< "  patternHash==" < patternHash.h1 < NL;
		if(candHash == patternHash){
			E < "match at position " < i < NL;
			++result;
		}
		
		if(i < to-1){
			prefsumLeft += basePowLeft * seqAt(i);
			prefsumRight += basePowRight * seqAt(i+pattSize);
			
			basePowLeft *= base;
			basePowRight *= base;
			patternHash *= base;
		}
	}
	
	
	// collect result
	PutInt(0,result);
	Send(0);
	
	if(myNodeId==0){
		result = 0;
		FOR(kk,numberOfNodes){
			int fromNode = Receive(-1);
			result += GetInt(fromNode);
		}
		O < result < NL;
	}
}