#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 pre(Poly as,int deg){ return Poly(as.begin(),as.begin()+min((int)as.size(),deg)); } 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]}); for(int i=1;ias.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; namespace FFT{ using dbl = double; struct num{ dbl x,y; num(){x=y=0;} num(dbl x,dbl y):x(x),y(y){} }; inline num operator+(num a,num b){ return num(a.x+b.x,a.y+b.y); } inline num operator-(num a,num b){ return num(a.x-b.x,a.y-b.y); } inline num operator*(num a,num b){ return num(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x); } inline num conj(num a){ return num(a.x,-a.y); } int base=1; vector rts={{0,0},{1,0}}; vector rev={0,1}; const dbl PI=acosl(-1.0); void ensure_base(int nbase){ if(nbase<=base) return; rev.resize(1<>1]>>1)+((i&1)<<(nbase-1)); rts.resize(1< &a,int n=-1){ if(n==-1) n=a.size(); assert((n&(n-1))==0); int zeros=__builtin_ctz(n); ensure_base(zeros); int shift=base-zeros; for(int i=0;i>shift)) swap(a[i],a[rev[i]>>shift]); for(int k=1;k fa; vector multiply(vector &a,vector &b){ int need=a.size()+b.size()-1; int nbase=0; while((1<(int)fa.size()) fa.resize(sz); for(int i=0;i>1);i++){ int j=(sz-i)&(sz-1); num z=(fa[j]*fa[j]-conj(fa[i]*fa[i]))*r; if(i!=j) fa[j]=(fa[i]*fa[i]-conj(fa[j]*fa[j]))*r; fa[i]=z; } fft(fa,sz); vector res(need); for(int i=0;i struct ArbitraryModConvolution{ using dbl=FFT::dbl; using num=FFT::num; vector multiply(vector as,vector bs){ int need=as.size()+bs.size()-1; int sz=1; while(sz fa(sz),fb(sz); for(int i=0;i<(int)as.size();i++) fa[i]=num(as[i].v&((1<<15)-1),as[i].v>>15); for(int i=0;i<(int)bs.size();i++) fb[i]=num(bs[i].v&((1<<15)-1),bs[i].v>>15); fft(fa,sz);fft(fb,sz); dbl ratio=0.25/sz; num r2(0,-1),r3(ratio,0),r4(0,-ratio),r5(0,1); for(int i=0;i<=(sz>>1);i++){ int j=(sz-i)&(sz-1); num a1=(fa[i]+conj(fa[j])); num a2=(fa[i]-conj(fa[j]))*r2; num b1=(fb[i]+conj(fb[j]))*r3; num b2=(fb[i]-conj(fb[j]))*r4; if(i!=j){ num c1=(fa[j]+conj(fa[i])); num c2=(fa[j]-conj(fa[i]))*r2; num d1=(fb[j]+conj(fb[i]))*r3; num d2=(fb[j]-conj(fb[i]))*r4; fa[i]=c1*d1+c2*d2*r5; fb[i]=c1*d2+c2*d1; } fa[j]=a1*b1+a2*b2*r5; fb[j]=a1*b2+a2*b1; } fft(fa,sz);fft(fb,sz); vector cs(need); using ll = long long; for(int i=0;i>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