#ifndef call_from_test #include using namespace std; using Int = long long; template inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template inline void chmax(T1 &a,T2 b){if(a struct FormalPowerSeries{ using Poly = vector; using Conv = function; Conv conv; FormalPowerSeries(Conv conv):conv(conv){} Poly add(Poly as,Poly bs){ int sz=max(as.size(),bs.size()); Poly cs(sz,T(0)); for(int i=0;i<(int)as.size();i++) cs[i]+=as[i]; for(int i=0;i<(int)bs.size();i++) cs[i]+=bs[i]; return cs; } Poly sub(Poly as,Poly bs){ int sz=max(as.size(),bs.size()); Poly cs(sz,T(0)); for(int i=0;i<(int)as.size();i++) cs[i]+=as[i]; for(int i=0;i<(int)bs.size();i++) cs[i]-=bs[i]; return cs; } Poly mul(Poly as,Poly bs){ return conv(as,bs); } Poly mul(Poly as,T k){ for(auto &a:as) a*=k; return as; } // F(0) must not be 0 Poly inv(Poly as,int deg){ assert(as[0]!=T(0)); Poly rs({T(1)/as[0]}); int sz=1; while(szas.size()) return Poly(); reverse(as.begin(),as.end()); reverse(bs.begin(),bs.end()); int need=as.size()-bs.size()+1; Poly ds=mul(as,inv(bs,need)); ds.resize(need); reverse(ds.begin(),ds.end()); return ds; } // F(0) must be 1 Poly sqrt(Poly as,int deg){ assert(as[0]==T(1)); int sz=1; T inv2=T(1)/T(2); Poly ss({T(1)}); while(sz struct Mint{ static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;}; Mint operator-(Mint a) const{return Mint(v)-=a;}; Mint operator*(Mint a) const{return Mint(v)*=a;}; Mint operator/(Mint a) const{return Mint(v)/=a;}; Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} bool operator <(const Mint a)const{return v constexpr T Mint::mod; template ostream& operator<<(ostream &os,Mint m){os< struct NTT{ static constexpr int md = bmds(X); static constexpr int rt = brts(X); using M = Mint; vector< vector > rts,rrts; void ensure_base(int n){ if((int)rts.size()>=n) return; rts.resize(n);rrts.resize(n); for(int i=1;i &as,bool f,int n=-1){ if(n==-1) n=as.size(); assert((n&(n-1))==0); ensure_base(n); for(int i=0,j=1;j+1>1;k>(i^=k);k>>=1); if(i>j) swap(as[i],as[j]); } for(int i=1;i multiply(vector as,vector bs){ int need=as.size()+bs.size()-1; int sz=1; while(sz multiply(vector as,vector bs){ vector am(as.size()),bm(bs.size()); for(int i=0;i<(int)am.size();i++) am[i]=M(as[i]); for(int i=0;i<(int)bm.size();i++) bm[i]=M(bs[i]); vector cm=multiply(am,bm); vector cs(cm.size()); for(int i=0;i<(int)cs.size();i++) cs[i]=cm[i].v; return cs; } }; template constexpr int NTT::md; template constexpr int NTT::rt; struct ArbitraryModConvolution{ using ll = long long; static NTT<0> ntt0; static NTT<1> ntt1; static NTT<2> ntt2; static constexpr int pow(int a,int b,int md){ int res=1; a=a%md; while(b){ if(b&1) res=(ll)res*a%md; a=(ll)a*a%md; b>>=1; } return res; } static constexpr int inv(int x,int md){ return pow(x,md-2,md); } inline void garner(int &c0,int c1,int c2,int m01,int MOD){ static constexpr int r01=inv(ntt0.md,ntt1.md); static constexpr int r02=inv(ntt0.md,ntt2.md); static constexpr int r12=inv(ntt1.md,ntt2.md); c1=(ll)(c1-c0)*r01%ntt1.md; if(c1<0) c1+=ntt1.md; c2=(ll)(c2-c0)*r02%ntt2.md; c2=(ll)(c2-c1)*r12%ntt2.md; if(c2<0) c2+=ntt2.md; c0+=(ll)c1*ntt0.md%MOD; if(c0>=MOD) c0-=MOD; c0+=(ll)c2*m01%MOD; if(c0>=MOD) c0-=MOD; } inline void garner(vector< vector > &cs,int MOD){ int m01 =(ll)ntt0.md*ntt1.md%MOD; int sz=cs[0].size(); for(int i=0;i multiply(vector as,vector bs,int MOD){ vector< vector > cs(3); cs[0]=ntt0.multiply(as,bs); cs[1]=ntt1.multiply(as,bs); cs[2]=ntt2.multiply(as,bs); size_t sz=as.size()+bs.size()-1; for(auto& v:cs) v.resize(sz); garner(cs,MOD); return cs[0]; } template decltype(auto) multiply(vector< Mint > am, vector< Mint > bm){ using M = Mint; vector as(am.size()),bs(bm.size()); for(int i=0;i<(int)as.size();i++) as[i]=am[i].v; for(int i=0;i<(int)bs.size();i++) bs[i]=bm[i].v; vector cs=multiply(as,bs,MOD); vector cm(cs.size()); for(int i=0;i<(int)cm.size();i++) cm[i]=M(cs[i]); return cm; } }; NTT<0> ArbitraryModConvolution::ntt0; NTT<1> ArbitraryModConvolution::ntt1; NTT<2> ArbitraryModConvolution::ntt2; //INSERT ABOVE HERE signed HAPPYQUERY_E(){ cin.tie(0); ios::sync_with_stdio(0); int n,m,q; cin>>n>>m>>q; vector ls(q),rs(q); for(int i=0;i>ls[i]>>rs[i],ls[i]--; vector as(n); for(int i=0;i>as[i]; if(as==vector(n,0)){ for(int i=0;i cs(n-m+1,0); for(int l:ls) cs[l]++; NTT<0> ntt; using M = NTT<0>::M; auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);}; FormalPowerSeries FPS(conv); vector ps(as.size()),qs(cs.size()); for(int i=0;i<(int)ps.size();i++) ps[i]=M(as[i]); for(int i=0;i<(int)qs.size();i++) qs[i]=M(cs[i]); auto bs=FPS.div(ps,qs); for(int i=0;i>n>>m; vector cs(n); for(int i=0;i>cs[i]; NTT<2> ntt; using M = NTT<2>::M; auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);}; FormalPowerSeries FPS(conv); const int deg=1<<18; vector as(deg,0); as[0]=M(1); for(int c:cs) as[c]-=M(4); auto bs=FPS.sqrt(as,deg); bs[0]+=M(1); vector vs({2}); auto ans=FPS.mul(vs,FPS.inv(bs,deg)); for(int i=1;i<=m;i++) cout<>k>>n; vector xs(n); for(int i=0;i>xs[i]; using M = Mint; ArbitraryModConvolution arb; auto conv=[&](auto as,auto bs){return arb.multiply(as,bs);}; FormalPowerSeries FPS(conv); const int sz=1<<17; vector bs(sz,M(0)); bs[0]=1; for(int x:xs) bs[x]-=M(1); cout<=md) a-=md; return a; } inline int mul(int a,int b){ return 1LL*a*b%md; } inline int pow(int a,int b){ int res=1; while(b){ if(b&1) res=mul(res,a); a=mul(a,a); b>>=1; } return res; } inline int sqrt(int a){ if(a==0) return 0; if(pow(a,(md-1)/2)!=1) return -1; int q=md-1,m=0; while(~q&1) q>>=1,m++; mt19937 mt; int z=mt()%md; while(pow(z,(md-1)/2)!=md-1) z=mt()%md; int c=pow(z,q),t=pow(a,q),r=pow(a,(q+1)/2); while(m>1){ if(pow(t,1<<(m-2))!=1) r=mul(r,c),t=mul(t,mul(c,c)); c=mul(c,c); m--; } return min(r,md-r); } signed LOJ_150(){ cin.tie(0); ios::sync_with_stdio(0); NTT<2> ntt; using M = NTT<2>::M; auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);}; FormalPowerSeries FPS(conv); int n,k; cin>>n>>k; vector F(n+1); for(int i=0;i<=n;i++) cin>>F[i].v; const int deg = 1<<17; auto as=FPS.log(FPS.mul(F,F[0].inv()),deg); auto bs=FPS.exp(FPS.mul(as,M((md-1)/2)),deg); M s(sqrt(F[0].v)); auto cs=FPS.integral(FPS.mul(bs,s.inv())); auto ds=FPS.exp(cs,deg); auto es=FPS.sub(F,ds); es[0]+=M(2); es[0]-=F[0]; auto fs=FPS.log(es,deg); fs[0]+=M(1); auto gs=FPS.log(fs,deg); auto hs=FPS.mul(gs,M(k)); auto is=FPS.exp(hs,deg); auto G=FPS.diff(is); for(int i=0;i