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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
#undef LOCAL2
#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;
#define oor >ostream&operator<<(ostream&o,
#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 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;}
sim> struct FIB{c x;};
sim> FIB<c> bifi(c x){return FIB<c>{x};}
sim oor FIB<c> f) {
	c v = f.x;
	assert(v >= 0);
	o << v << " = ";
	vector <c> fibs = {1, 2};
	while (*fibs.rbegin() + *(fibs.rbegin() + 1) <= v)
		fibs.push_back(*fibs.rbegin() + *(fibs.rbegin() + 1));
	while (fibs.size() >= 2u && fibs.back() > v) fibs.pop_back();
	FORD(i, (int)fibs.size() - 1, 0) {
		if (v >= fibs[i]) {
			o << 1;
			v -= fibs[i];
		}
		else
			o << 0;
	}
	ros << "_" << fibs.size() - 1;
}
#define fibi(r) ngy(bifi(r), #r)
#define XREP(i,n) for(int i = 0; i < int(n); ++i)
/*Precision error max_ans/1e15 (2.5e18) for (long) doubles.
So integer rounding works for doubles with answers 0.5*1e15,
e.g. for sizes 2^20 and RANDOM positive integers up to 45k.
Those values assume DBL_MANT_DIG=53 and LDBL_MANT_DIG=64.
For input in [0, M], you can decrease everything by M/2.
If there are many small vectors, uncomment "BRUTE FORCE".*/
typedef double dou; // 'long double' is 2.2 times slower
struct C {
	dou real, imag;
	C operator * (const C & he) const {
		return C{real * he.real - imag * he.imag,
				real * he.imag + imag * he.real};
	}
	void operator += (const C & he) {
		real += he.real; imag += he.imag;
	}
};
void dft(vector<C> & a, bool rev) {
	const int n = a.size();
	for(int i = 1, k = 0; i < n; ++i) {
		for(int bit = n / 2; (k ^= bit) < bit; bit /= 2);;;
		if(i < k) swap(a[i], a[k]);
	}
	for(int len = 1, who = 0; len < n; len *= 2, ++who) {
		static vector<C> t[30];
		vector<C> & om = t[who];
		if(om.empty()) {
			om.resize(len);
			const dou ang = 2 * acosl(0) / len;
			XREP(i, len) om[i] = i%2 || !who ?
					C{cos(i*ang), sin(i*ang)} : t[who-1][i/2];
		}
		for(int i = 0; i < n; i += 2 * len)
			XREP(k, len) {
				 const C x = a[i+k], y = a[i+k+len]
						* C{om[k].real, om[k].imag * (rev ? -1 : 1)};
				a[i+k] += y;
				a[i+k+len] = C{x.real - y.real, x.imag - y.imag};
			}
	}
	if(rev) XREP(i, n) a[i].real /= n;
}
template<typename T>vector<T> multiply(const vector<T> & a, const vector<T> & b, bool split = false) {
	if(a.empty() || b.empty()) return {};
	int n = a.size() + b.size();
	vector<T> ans(n - 1);
	/* if(min(a.size(),b.size()) < 190) { // BRUTE FORCE
		XREP(i, a.size()) XREP(j, b.size()) ans[i+j] += a[i]*b[j];
		return ans; } */
	while(n&(n-1)) ++n;
	// http://codeforces.com/blog/entry/48417
	auto speed = [&](const vector<C> & w, int i, int k) {
		int j = i ? n - i : 0, r = k ? -1 : 1;
		return C{w[i].real + w[j].real * r, w[i].imag
				- w[j].imag * r} * (k ? C{0, -0.5} : C{0.5, 0});
	};
	if(!split) { // standard fast version
		vector<C> in(n), done(n);
		XREP(i, a.size()) in[i].real = a[i];
		XREP(i, b.size()) in[i].imag = b[i];
		dft(in, false);
		XREP(i, n) done[i] = speed(in, i, 0) * speed(in, i, 1);
		dft(done, true);
		XREP(i, ans.size()) ans[i] = is_integral<T>::value ?
				llround(done[i].real) : done[i].real;
	//XREP(i,ans.size())err=max(err,abs(done[i].real-ans[i]));
	}
	else { // Split big INTEGERS into pairs a1*M+a2,
		const T M = 150; // where M = sqrt(max_absvalue).
		vector<C> t[2]; // This version is 2.2-2.5 times slower.
		XREP(x, 2) {
			t[x].resize(n);
			auto & in = x ? b : a;
			XREP(i, in.size()) t[x][i]=C{dou(in[i]%M), dou(in[i]/M)};
			dft(t[x], false);
		}
		T mul = 1;
		for(int s = 0; s < 3; ++s, mul *= M) {
			vector<C> prod(n);
			XREP(x, 2) XREP(y, 2) if(x + y == s) XREP(i, n)
				prod[i] += speed(t[0], i, x) * speed(t[1], i, y);
			dft(prod, true);
			XREP(i, ans.size()) ans[i]+= llround(prod[i].real)*mul;
		}
	}
	return ans;
}
sim> ll calc_mod(const vector <c> &d, ll mod) {
	ll a = 1, b = 1;
	ll val = 0;
	for (c x : d) {
		if (x) val = (val + mul(x, b, mod)) % mod;
		ll v = (a + b) % mod;
		a = b;
		b = v;
	}
	return val;
}
sim> void assert_good(const vector <c> &d) {
	REP(i, (int) d.size() - 1)
		assert(d[i] * d[i + 1] == 0);
	for (int x : d) assert(x == 0 || x == 1);
	assert(!d.empty() && d.back() == 1);
}
sim> void fix2(vector <c> &f) {
	loc (ll mod = rand() % (ll) 1e18 + 1;
		ll v = calc_mod(f, mod);
	)
	f.resize(f.size() + 80);
	int n = f.size();
	bool any = true;
	loc(int turns = 0);
	while (any) {
		loc(turns++);
		any = false;
		REP(i, n - 2) {
			c push = min(f[i], f[i + 1]);
			if (push) any = true;
			f[i] -= push;
			f[i + 1] -= push;
			f[i + 2] += push;
		}
		REP(i, n - 2) {
			c push = f[i] / 2;
			if (push) any = true;
			if (i == 0) {
				f[i] -= 2 * push;
				f[i + 1] += push;
			}
			else if (i == 1) {
				f[i - 1] += push;
				f[i] -= 2 * push;
				f[i + 1] += push;
			}
			else {
				f[i - 2] += push;
				f[i] -= 2 * push;
				f[i + 1] += push;
			}
		}
	}
	while (f.back() == 0) f.pop_back();
	debug(imie(turns));
	loc(ll v2 = calc_mod(f, mod);
		assert(v == v2);
		assert_good(f);
	)
}
vector <ll> fib_mul(const vector <int> &a, const vector <int> &b) {
	debug("start");
	vector <ll> ans(a.size() + b.size() + 40);
	loc(ll mod = rand() % (ll) 1e18 + 1;)
	vector <int> m1 = multiply(a, b);
	#define NEXT
	#ifndef NEXT	
		for (int x = (int) m1.size() - 1; x >= 0; --x)
			ans[x] = m1[x] + ans[x + 4];
		ans[0] += ans[3];
	#endif
	ll at_neg1 = 0;
	vector <int> as[2], bs[2];
	vector <ll> ans2(ans.size());
	REP(i, a.size()) as[i & 1].push_back(a[i]);
	REP(i, b.size()) bs[i & 1].push_back(b[i]);
	reverse(ALL(bs[0]));
	reverse(ALL(bs[1]));
	// debug(imie(a), imie(b));
	REP(ap, 2) REP(bp, 2) {
		// debug(imie(ap), imie(bp));
		vector <int> m = multiply(as[ap], bs[bp]);
		// debug(arr(as, ap), arr(bs, bp), imie(m));
		REP(i, (int)m.size()) {
			int diff = 2 * (i - bs[bp].size() + 1) + ap - bp;
			int low = diff < 0 ? ap : bp;
			int s2 = abs(diff) + 2 * low - 4;
			// int should = 0;
			// REP(aa, (int)a.size()) REP(bb, (int)b.size()) {
				// if (aa - bb == diff && low == (min(aa, bb) & 1)) {
					// debug(arr(a, aa) * arr(b, bb));
					// should += a[aa] * b[bb];
				// }
			// }
			// debug(imie(diff), imie(low), imie(s2), arr(m, i), imie(should));
			// assert(m[i] == should);
#ifdef NEXT
			//debug(imie(s2), arr(m, i));
			if (s2 >= -1)
				m1[max(0, s2)] -= m[i];
#else
			for (int x = s2; x >= -1; x -= 4)
				ans[max(0, x)] -= m[i];
#endif
			if (low)
				ans2[max(0, s2 + 1)] += m[i];
		}
	}
#ifdef NEXT
	for (int x = (int) m1.size() - 1; x >= 0; --x)
		ans[x] = m1[x] + ans[x + 4];
	ans[0] += ans[3] + at_neg1;
#endif
	REP(i, ans.size()) ans[i] += ans2[i];
	// debug(imie(ans), " ?= {6, 6, 4, 4, 3, 2, 1}");
	// REP(i, (int) a.size()) REP(j, (int) b.size()) {
		// if (a[i] && b[j]) {
			// int absdiff = abs(i - j);
			// int low = min(i, j) & 1;
			// int s2 = absdiff + 2 * low - 4;
			// for (int x = s2; x >= -1; x -= 4)
				// ans[max(0, x)]--;
			// if (low)
				// ans[max(0, s2 + 1)]++;
		// }
	// }
	// debug(imie(a), imie(b), imie(ans));
	debug("start fix");
	fix2(ans);
	debug("end fix");
#if defined(LOCAL) || defined(LOCAL2)
	ll amod = calc_mod(a, mod);
	ll bmod = calc_mod(b, mod);
	ll cmod = calc_mod(ans, mod);
	assert(mul(amod, bmod, mod) == cmod);
#endif
	rans;
}
vector <int> get() {
	int l;
	scanf("%d", &l);
	vector <int> ans(l);
	REP(i, l) scanf("%d", &ans[i]);
	rans;
}
int main() {
#warning Jak wzorcówka jest równie syfna jak mój rozw, to się pogniewamy xD
	int t;
	scanf("%d", &t);
	while (t--) {
		vector <int> a = get(), b = get();
		vector <ll> c = fib_mul(a, b);
		printf("%d", (int) c.size());
		for (ll x : c) printf(" %lld", x);
		printf("\n");
	}
}