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//Konrad Paluszek,University of Warsaw(former XIV LO Staszic)
//it's nice to stick a fork into an open socket
//clock says it's time to sleep
//our getppid() in heaven, hallowed by ttyname
#ifndef LOCAL
#pragma GCC optimize("O3")
#endif
#define TIME (chrono::steady_clock::now().time_since_epoch().count())
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define xfm(a,b)a##b
#define xwb(a,b)xfm(a,b)
#define _ xwb(nvj,__LINE__)
#define FOR(i,b,e)for(urs((b)+(e))i=(b);i<=(e);++i)
#define REP(i,n)for(urs(n)i=0;i<(n);++i)
#define FORD(i,b,e)for(urs((b)+(e))i=(b);i>=(int)(e);--i)
#define UNTIL(t)while(clock()<(t)*CLOCKS_PER_SEC)
#define PER(r...)for(bool _=1;_||next_permutation(r);_=false)
#define ALL(r)(r).begin(),(r).end()
#define FS(r)r.first,r.second
#define sim template<class c
#define ros return o
#define rans return ans
#define forbits(i,m)if(m)for(urs(m)i=ctz(m),i##nvj=m;i##nvj;i##nvj^=((urs(m))1<<i),i=ctz(i##nvj))
#define fordbits(i,m)if(m)for(urs(m)i=8*sizeof(m)-clz(m)-1,i##nxd=m;i##nxd;i##nxd^=((urs(m))1<<i),i=8*sizeof(m)-clz(i##nxd)-1)
#define ksets(t, m, k, n) for (t m = (((t)1 << (k)) - 1); m < ((t)1 << (n)); m = nux(m))
#define urs(r...)typename decay<decltype(r)>::type
#define hur(f,g,r)sim>int f(c a){if(sizeof(c)==16)return r;if(sizeof(c)==8)return g##ll(a);return g(a);}
#define pwq(t,i) int clz(t x){return clz<int>(x)-i;}
using namespace __gnu_pbds;using namespace std;using ll=long long;using ld=long double;using ull=unsigned long long;using pii=pair<int,int>;using pll=pair<ll,ll>;using vpii=vector<pii>;using unt=unsigned int;sim>using min_queue=priority_queue<c,vector<c>,greater<c>>;sim>using ordered_set=tree<c,null_type,less<c>,rb_tree_tag,tree_order_statistics_node_update>;hur(popc,__builtin_popcount,popc<ull>(a)+popc<ull>(a>>64))hur(ctz,__builtin_ctz,(ull)a?ctz<ull>(a):64+ctz<ull>(a>>64))hur(clz,__builtin_clz,a>>64?clz<ull>(a>>64):64+clz<ull>(a))pwq(short,16)pwq(uint16_t,16)pwq(char,24)pwq(int8_t,24)pwq(uint8_t,24)sim,class N>bool mini(c&o,const N&h){if(o>h)ros=h,1;return 0;}sim,class N>bool maxi(c&o,const N&h){if(o<h)ros=h,1;return 0;}sim,class n>using gyv=c;
#ifdef LOCAL
#define loc(r...)r
#define onl(r...)
#define azm(r)sim,class n,class l,class...v>bool emz1(const r<c,n,v...>&o,l b){ros.count(b);}sim,class n,class l,class...v>const n&emz2(const r<c,n,v...>&o,l b){ros.find(b)->second;}
#define oor >ostream&operator<<(ostream&o,
#define debug(c...)::dor(1,vqx(__LINE__,__FUNCTION__,__PRETTY_FUNCTION__),c)
#define rcu m);}g(+)g(-)g(*)g(/)g(%)g(<<)g(>>)g(^)g(|)g(&)g(>=)g(<=)g(>)g(<)g(!=)g(==)
#define zub(h,t,n...)class N>auto operator h(n u)->nep<urs(t)>{return ngy(t,
#define g(o)template<zub(o,v o u,N)tfj(bte(*this))+" " #o " "+tfj(bte(u)),m);}
sim>gyv<int,typename c::value_type>dud(int x);sim>char dud(...);struct kav;sim>struct lfu;sim> struct jat;struct kav{static const int d=0;};sim>struct lfu{static const int d=jat<typename c::value_type>::d + 1;};sim>struct jat{static const int d=conditional<sizeof(dud<c>(0))==1,kav,lfu<c>>::type::d;};sim,class n>struct jat<pair<c,n>>{static const int d=jat<c>::d>jat<n>::d?jat<c>::d:jat<n>::d;};template<>struct jat<string>{static const int d=0;};
vector <pair <string, string> > repl = {{"std::", ""}, {"__debug::", ""}, {"long long unsigned int", "ull"}, {"long unsigned int", "size_t"}, {"unsigned int", "unt"}, {"long long int", "ll"}, {"vector<pair<int, int> >", "vpii"}, {"pair<int, int>", "pii"}, {"pair<long double, long double>", "pdd"}, {"long double", "ld"}};
string xif(string r) {string o;int d=0;for(char c:r) if(c=='[')d++;else if(c==']')d--;else if(d)o+=c;for(auto p:repl)while(true){unt f=o.find(p.first);if(f<o.size())o.replace(f,p.first.size(),p.second);else break;}if(o.size())o=" "+o;ros;}
sim>c&lum(c&o){ros;}int lum(int8_t o){ros;}unt lum(uint8_t o){ros;}int uuv=6;void set_pre(int x){uuv=x;}sim>struct yda{c x;ll p,q,r,s;};sim>yda<typename std::decay<c>::type>nyb(c x,ll p,ll q,ll r,ll s){return{x,p,q,r,s};}azm(map)azm(unordered_map)sim>bool emz1(const c&a,ll o){ros>=0&&o<(ll)a.size();}sim>auto emz2(const c&o,ll x)->decltype(o[x]){ros[x];}sim>bool emz1(c*a,ll o){ros>=0;}sim>c&emz2(c*o,ll b){ros[b];}template<size_t n>bool emz1(const bitset<n>&,ll o){ros>=0&&o<(ll)n;}template<size_t n>int emz2(const bitset<n>&o,ll b){ros[b];}string tfj(string o){for(char x:o)if(x=='=')return"("+o+")";ros;}string vqx(int l,string f,string pf){stringstream o;o<<"\033[1;"<<30+l%8<<"m"<<f<<xif(pf)<<"#"<<l<<": \033["<<30+l%7+(l%7>=l%8)<<"m";ros.str();}ostream&operator<<(ostream&o,__int128 x){int D[50],c=0;if(x<0)o<<"-",x=-x;do{D[c++]=x%10;x/=10;}while(x);while(c)o<<D[--c];ros;}ostream&operator<<(ostream&o,__uint128_t x){int D[50],c=0;do{D[c++]=x%10;x/=10;}while(x);while(c)o<<D[--c];ros;}ostream&operator<<(ostream&o,__float128 x){ros<<(ld)x;}sim,class N oor pair<c,N>u){ros<<"<"<<lum(u.first)<<", "<<lum(u.second)<<">";}sim,typename=typename enable_if<!is_same<c,string>::value,urs(c().end())>::type oor c u){int q=0;o<<"{";for(auto e:u)o<<", "+2*!q++<<lum(e);ros<<"}_"<<q;}void dor(bool x){cerr<<dec<<"\033[0m"<<endl;}sim,class...N>void dor(int w,c x,N...y){cerr<<setprecision(uuv)<<boolalpha<<x<<"; "+2*w;dor(0,y...);}sim>string bte(c u){stringstream o;o<<setprecision(uuv)<<boolalpha<<lum(u);ros.str();}sim>struct nep;sim>c yyo(nep<c>);sim>nep<c>ngy(c,string,int m=0);sim>c yyo(c o){ros;}sim>struct nep{c v;string d;int m;nep<c>mask(){return ngy(v,d,1);}template<zub([],v[yyo(u)],N)d+"["+bte(u)+"]",rcu};sim>nep<c>ngy(c v,string d,int m){return nep<c>{v,d,m};}sim>c yyo(nep<c>o){ros.v;}sim>int uhn(c){return 0;}sim>int uhn(nep<c>o){ros.m;}
#undef g
#define ckx(o)template<zub(o,o yyo(u),nep<N>)#o+tfj(bte(u)),u.m);}
#define g(o)sim,zub(o,yyo(p)o u.v,c p,nep<N>)tfj(bte(p))+" " #o " "+tfj(bte(u)),uhn(p)+u.m);}
#define ccy(r...)sim>class enable_if<r is_integral<c>::value,string>::type ema(c u){
#define qel(t)sim,class d,class...e oor t<c,d,e...>r){ros<<*(d*)&r;}
qel(queue)qel(priority_queue)qel(stack)ccy(!)return bte(u);}ccy()stringstream o;o<<"[";int q=0;forbits(i,u)o<<", "+2*!q++<<lum(i);ros.str()+"]";}sim>string bte(nep<c>o){string v=(o.m?ema(o.v):bte(o.v));if(v==o.d)ros.d;ros.d+" = "+v;}sim oor nep<c>m){ros<<bte(rcu sim>nep<c>ngy(nep<c>o,string d="",int m=0){ros;}ckx(+)ckx(-)ckx(!)ckx(~)sim oor yda<c>M){if(M.p>=M.q||M.r>=M.s)ros<<"[------]";int l=0;stringstream p;vector<vector<string>>X;vector<int>Y(M.s-M.r,1);FOR(i,M.p,M.q-1){maxi(l,(int)bte(i).size());X.emplace_back();if(emz1(M.x,i)){auto V=emz2(M.x,i);FOR(j,M.r,M.s-1){if(emz1(V,j)){auto Q=emz2(V,j);X.back().push_back(bte(Q));maxi(Y[j-M.r],(int)X.back().back().size());}else X.back().push_back("3Ju+");}}}FOR(i,M.p,M.q-1){p<<"\n"<<setw(l)<<i<<": ";if(X[i-M.p].size())FOR(j,M.r,M.s-1){if(X[i-M.p][j-M.r]=="3Ju+")REP(_,Y[j-M.r])p<<"-";else p<<setw(Y[j-M.r])<<X[i-M.p][j-M.r];p<<"; ";}}p<<"\n";ros<<p.str();}vector<string>fdn;struct bcx{bcx(){fdn.push_back("");}~bcx(){fdn.pop_back();}};void imx(string m){cerr<<m<<"STACK TRACE: "<<dec<<"\033[0m"<<endl;for(auto x:fdn)cerr<<"\t"<<x<<"\033[0m"<<endl;}void ctm(bool r){fdn.back()+="\033[m";}sim,class...n>void ctm(bool r,c x,n...y){fdn.back()+=bte(x)+("; "+2*r);ctm(0,y...);}
#undef g
#define imie(a...) ngy(a,#a)
#define imask(a...) ngy(a,#a,1)
#define ra3(u,g,c) ngy(list<urs((u)[0])>(begin(u)+yyo(g),begin(u)+yyo(c)),#u "["+bte(g)+"..."+bte(c)+")")
#define ra2(i,j)ngy(list<urs(*(i))>(i,j),"[" #i "..." #j ")")
#define zoz(a,b,c,d,e...) d
#define range(r...) zoz(r,ra3,ra2)(r)
#define arr(a, i) imie(a)[imie(i)]
#define arr2(a, i, j) imie(a)[imie(i)][imie(j)]
#define print_stack(r...)::imx(vqx(__LINE__,__FUNCTION__,__PRETTY_FUNCTION__))
#define mark_stack(r...)bcx _;::ctm(1,vqx(__LINE__,__FUNCTION__,__PRETTY_FUNCTION__),r)
#define dump(a,i,j,k,q)ngy(nyb(a,yyo(i),yyo(j),yyo(k),yyo(q)),#a "["+bte(imie(i))+".."+bte(imie(j))+")["+bte(imie(k))+".."+bte(imie(q))+")")
#else
#define loc(...)
#define onl(r...)r
#define debug(...)
#define print_stack(...)
#define mark_stack(...)
#define set_pre(...)
#endif
#define next nexT
#define prev preV
#define tree trEE
#define left lefT
#define right righT
#define div diV
#define y1 y_1
ull mix(ull o){o+=0x9e3779b97f4a7c15;o=(o^(o>>30))*0xbf58476d1ce4e5b9;o=(o^(o>>27))*0x94d049bb133111eb;ros^(o>>31);}ull SALT=0x7a14a4b0881ebf9,tqu=0x7a14a4b0881ebf9;ull my_rand(){return tqu=mix(tqu);}void my_srand(ull x){SALT=tqu=x;}const int inf = 1023400000;const ll llinf=1234567890000000000ll;
#define rand my_rand
#define srand my_srand
#define random_shuffle(r...)random_shuffle(r,[](int _){return my_rand()%_;})
sim>inline c nux(c m){if(!m)return numeric_limits<c>::max();c A=m&-m;c B=~((A-1)^m);c C=B&-B;c D=(C>>(1+ctz(A)))-1;return C|(m&~(C-1))|D;}__attribute__((no_sanitize_undefined))ll mul(ll a,ll b,ll m){ll q=a*(ld)b/m;ll o=a*b-q*m;o%=m;if(o<0)o+=m;ros;}sim>void unq(c&x){x.resize(unique(ALL(x))-x.begin());}sim>c gcd(c o,c b){while(o&&b){int x=ctz(o),y=ctz(b);if(x>y)o>>=x-y;else b>>=y-x;if(o>b)o-=b;else b-=o;}ros?o:b;}sim>c lcm(c o,c b){ros/gcd(o,b)*b;}
sim>typename enable_if<is_integral<c>::value,ull>::type my_hash(c x){
	if(sizeof(c)>8) return mix((ull)x^SALT)^mix((ull)(x>>64)^SALT);
	return mix(x^SALT);
}
template<size_t N>ull my_hash(const bitset<N>&x){
	return mix(hash<bitset<N>>()(x)^SALT);
}
sim,class n>ull my_hash(const pair<c,n>&);
sim>gyv<ull,typename c::value_type>my_hash(const c&x){
	ull o=SALT;
	for(auto&d:x)o=mix(o^my_hash(d));
	ros;
}
sim,class n>ull my_hash(const pair<c,n>&x){return mix(my_hash(x.first))^my_hash(x.second);}
sim>struct my_hasher{size_t operator()(const c&o)const{return my_hash(o);}};
sim,class m>using _un0rDer3d_M4P=loc(unordered_map)onl(cc_hash_table)<c,m,my_hasher<c>>;
#define unordered_map _un0rDer3d_M4P
string join(const vector<string>&x){stringstream ans;ans<<"\n";for(const string&c:x)ans<<c<<"\n";return ans.str();}
sim,class F>auto get(F f,c x)->decltype(f[x]){return f[x];}
sim,class F>auto get(F f,c x)->decltype(f(x)){return f(x);}
vector<string>sp(string x){vector<string>ans(1);for(char c:x){if(c=='\n')ans.emplace_back();else ans.back().push_back(c);}rans;}
sim,class F,class G>vector<string>draw_tree_rec(c t,const c*p,F s,G d){auto C=get(s,t);auto r=sp(d(t));int lr=0;for(auto&x:r)maxi(lr,(int)x.size());if(C.empty()||(p&&C==urs(C){*p})){for(auto&q:r)q.resize(lr,' ');return r;}vector<string>ans(0);int le=0;vector<int>vs;bool prev=false;for(c x:C){if(p&&x==*p)continue;auto curr=draw_tree_rec(x,&t,s,d);for(int i=ans.size();i<(int)curr.size();++i)ans.push_back(string(le,' '));if(prev){for(int i=0;i<(int)ans.size();++i)ans[i]+=' ';le++;}prev=true;for(int i=0;i<(int)curr.size();++i)ans[i]+=curr[i];for(int i=curr.size();i<(int)ans.size();++i)ans[i]+=string(curr[0].size(),' ');vs.push_back(le+curr[0].size()/2);le+=curr[0].size();}if(lr>le){int ladd=(lr-le)/2,radd=(lr-le+1)/2;for(int&x:vs)x+=ladd;for(int i=0;i<(int)ans.size();++i)ans[i]=string(ladd,' ')+ans[i]+string(radd,' ');le=lr;}int up_i=le/2;int pos=0;string bot;for(int i=0;i<le;++i){bool down=false,up=i==up_i,in=false;if(pos==(int)vs.size())in=i<up_i;else if(i==vs[pos]){in=down=true;pos++;}else if(pos==0)in=i>up_i;else if(pos==(int)vs.size())in=i<up_i;else in=true;if(up&&down)bot+='+';else if(up)bot+='^';else if(down)bot+='v';else if(in)bot+='-';else bot+=' ';}int ladd=(le-lr)/2;for(auto&q:r){q=string(ladd,' ')+q;q+=string(le-q.size(),' ');}r.push_back(bot);ans.insert(ans.begin(),ALL(r));for(int i=1;i<(int)ans.size();++i)assert(ans[i].size()==ans[0].size());rans;}
sim,class F,class G>string draw_tree(c t,F s,G d){return join(draw_tree_rec(t,(c*)0,s,d));}
sim,class F>string draw_tree(c t,F s){return draw_tree(t,s,[](c x){return bte(x);});}
sim,class F,class G>string draw_tree(c t,c p,F s,G d){return join(draw_tree_rec(t,&p,s,d));}
sim,class F>string draw_tree(c t,c p,F s){return draw_tree(t,p,s,[](c x){return bte(x);});}
#define by_parents(p,n) [&](int xwb(vsu,__LINE__)){vector<int>o;for(int _=0;_<=(n);++_)if(p[_]==xwb(vsu,__LINE__)&&_!=xwb(vsu,__LINE__))o.push_back(_);ros;}
pii operator+(pii a, pii b) {return {a.first + b.first, a.second + b.second};}
pii operator-(pii a, pii b) {return {a.first - b.first, a.second - b.second};}
set <pii> up, down;
bool in_rec(pii a, pii x, pii b) {
	return a.first <= x.first && x.first <= b.first && a.second <= x.second && x.second <= b.second;
}
int n, m, q;
bool on_path(pii x, const set <pii> &path) {
	auto it = path.lower_bound(x);
	assert(it != path.end());
	if (*it == x) return true;
	auto it2 = it;
	it2--;
	return in_rec(*it2, x, *it);
}
const int nax = 1e5 + 44;
set <int> by_x[nax], by_y[nax];
struct board {};
#ifdef LOCAL
ostream &operator<<(ostream &o, board) {
	o << imie(up) << " " << imie(down) << "\n";
	REP(i, n) {
		REP(j, m) {
			bool blocked = by_x[i].count(j);
			assert(blocked == by_y[j].count(i));
			bool on_up = on_path(pii(i, j), up);
			bool on_down = on_path(pii(i, j), down);
			o << ".duiXDUI"[blocked * 4 + on_up * 2 + on_down];
		}
		o << "\n";
	}
	ros;
}
#endif
void assert_san(string which, const set <pii> &s) {
	// debug(which, s);
	assert(*s.begin() == pii(0, 0));
	assert(*s.rbegin() == pii(n - 1, m - 1));
	vpii path;
	for (auto x : s) path.push_back(x);
	int l = path.size();
	REP(i, l - 1) {
		pii a = path[i], b = path[i + 1];
		assert(a < b);
		assert(a.first == b.first || a.second == b.second);
	}
	REP(i, l - 2) {
		pii a = path[i], b = path[i + 1], c = path[i + 2];
		assert(a.first != b.first || b.first != c.first);
		assert(a.second != b.second || b.second != c.second);
	}
}
void assert_san() {
	loc(assert_san("up", up));
	loc(assert_san("down", down));
}
bool on_board(pii x) {
	return x.first >= 0 && x.second >= 0 && x.first < n && x.second < m;
}
bool is_blocked(pii p) {
	assert(on_board(p));
	return by_x[p.first].count(p.second);
}
void assert_free() {
	#ifdef LOCAL
	REP(i, n) REP(j, m) if (is_blocked(pii(i, j))) {
		assert(!on_path(pii(i, j), up));
		assert(!on_path(pii(i, j), down));
	}
	#endif
}
pii find_N(pii p) {
	auto it = by_y[p.second].upper_bound(p.first);
	if (it == by_y[p.second].begin()) return {-1, -1};
	it--;
	return {*it, p.second};
}
pii find_S(pii p) {
	auto it = by_y[p.second].lower_bound(p.first);
	if (it == by_y[p.second].end()) return {nax, nax};
	return {*it, p.second};
}
pii find_E(pii p) {
	auto it = by_x[p.first].lower_bound(p.second);
	if (it == by_x[p.first].end()) return {nax, nax};
	return {p.first, *it};
}
pii find_W(pii p) {
	auto it = by_x[p.first].upper_bound(p.second);
	if (it == by_x[p.first].begin()) return {-1, -1};
	it--;
	return {p.first, *it};
}
void xor_to(set <pii> &s, pii v) {
	assert(on_board(v));
	if (v == pii(0, 0) || v == pii(n - 1, m - 1)) return;
	auto it = s.find(v);
	if (it == s.end()) s.insert(v);
	else s.erase(it);
}
void rec_rem_up(pii x) {
	// debug(imie(x));
	assert(on_board(x));
	auto it = up.lower_bound(x);
	if (*it == x) {
		auto pr = it, ne = it;
		pr--;
		ne++;
		if (pr->first == it->first) {
			pii a = *it;
			pii b = a, c = a, d = a;
			b.second--;
			c.first++;
			d.second--;
			d.first++;
			up.erase(a);
			xor_to(up, b);
			xor_to(up, c);
			up.insert(d);
			assert_san();
			if (is_blocked(d))
				rec_rem_up(d);
		}
		else {
			pii prv = *pr, itv = *it, nev = *ne;
			up.erase(prv);
			up.erase(itv);
			up.erase(nev);
			pii newit = itv + pii(1, -1);
			up.insert(newit);
			xor_to(up, prv + pii(0, -1));
			xor_to(up,nev + pii(1, 0));
			assert_san();
			if (is_blocked(newit))
				rec_rem_up(newit);
			else {
				pii r1 = find_N(newit);
				pii r2 = find_E(newit);
				if (on_board(r1) && on_path(r1, up))
					rec_rem_up(r1);
				if (on_board(r2) && on_path(r2, up))
					rec_rem_up(r2);
			}
		}
	}
	else {
		auto it2 = it;
		it--;
		pii pr = *it, ne = *it2;
		assert(in_rec(pr, x, ne));
		if (pr.first == x.first) {
			up.erase(ne);
			xor_to(up, ne + pii(1, 0));
			xor_to(up, x + pii(0, -1));
			up.insert(x + pii(1, -1));
			assert_san();
			pii go = find_E(x + pii(1, -1));
			if (on_board(go) && on_path(go, up))
				rec_rem_up(go);
		}
		else {
			up.erase(pr);
			xor_to(up, pr + pii(0, -1));
			xor_to(up, x + pii(1, 0));
			up.insert(x + pii(1, -1));
			assert_san();
			pii go = find_N(x + pii(1, -1));
			if (on_board(go) && on_path(go, up))
				rec_rem_up(go);
		}
	}
}
void rec_rem_down(pii x) {
	// debug(imie(x));
	assert(on_board(x));
	auto it = down.lower_bound(x);
	if (*it == x) {
		// debug("corner");
		auto pr = it, ne = it;
		pr--;
		ne++;
		if (pr->second == it->second) {
			// debug("case 1");
			pii a = *it;
			pii b = a, c = a, d = a;
			b.first--;
			c.second++;
			d.first--;
			d.second++;
			xor_to(down, b);
			xor_to(down, c);
			down.erase(a);
			down.insert(d);
			assert_san();
			if (is_blocked(d))
				rec_rem_down(d);
		}
		else {
			// debug("case 2");
			pii prv = *pr, itv = *it, nev = *ne;
			down.erase(prv);
			down.erase(itv);
			down.erase(nev);
			pii newit = itv + pii(-1, 1);
			down.insert(newit);
			xor_to(down, prv + pii(-1, 0));
			xor_to(down, nev + pii(0, 1));
			assert_san();
			if (is_blocked(newit))
				rec_rem_down(newit);
			else {
				pii r1 = find_S(newit);
				pii r2 = find_W(newit);
				if (on_board(r1) && on_path(r1, down))
					rec_rem_down(r1);
				if (on_board(r2) && on_path(r2, down))
					rec_rem_down(r2);
			}
		}
	}
	else {
		auto it2 = it;
		it--;
		pii pr = *it, ne = *it2;
		assert(in_rec(pr, x, ne));
		if (pr.first == x.first) {
			down.erase(pr);
			xor_to(down, pr + pii(-1, 0));
			xor_to(down, x + pii(0, 1));
			down.insert(x + pii(-1, 1));
			assert_san();
			pii go = find_W(x + pii(-1, 1));
			if (on_board(go) && on_path(go, down))
				rec_rem_down(go);
		}
		else {
			down.erase(ne);
			xor_to(down, ne + pii(0, 1));
			xor_to(down, x + pii(-1, 0));
			down.insert(x + pii(-1, 1));
			assert_san();
			pii go = find_S(x + pii(-1, 1));
			if (on_board(go) && on_path(go, down))
				rec_rem_down(go);
		}
	}
}
int main() {
	scanf("%d%d%d", &n, &m, &q);
	int x = 0;
	up = {pii{0, 0}, pii{0, m - 1}, pii{n - 1, m - 1}};
	down = {pii{0, 0}, pii{n - 1, 0}, pii{n - 1, m - 1}};
	REP(_, q) {
		int r, c, z;
		scanf("%d%d%d", &r, &c, &z);
		r ^= x;
		c ^= x;
		r %= n;
		c %= m;
		// debug("decoded", imie(r), imie(c));
		pii wh = {r, c};
		bool on_1 = on_path(wh, up), on_2 = on_path(wh, down);
		if (on_1 && on_2) {
			x ^= z;
			printf("TAK\n");
			continue;
		}
		by_x[r].insert(c);
		by_y[c].insert(r);
		printf("NIE\n");
		// debug(imie(on_1), imie(on_2));
		if (on_1)
			rec_rem_up(wh);
		if (on_2)
			rec_rem_down(wh);
		// debug(board());
		assert_san();
		assert_free();
	}
}