#define _USE_MATH_DEFINES #include using namespace std; //template #define rep(i,a,b) for(int i=(a);i<(b);i++) #define ALL(v) (v).begin(),(v).end() typedef long long int ll; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12; templateinline bool chmax(T& a,T b){if(ainline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} templateinline T get(){ char c=getchar(); bool neg=(c=='-'); T res=neg?0:c-'0'; while(isdigit(c=getchar()))res=res*10+(c-'0'); return neg?-res:res; } templateinline void put(T x,char c='\n'){ if(x<0)putchar('-'),x*=-1; int d[20],i=0; do{d[i++]=x%10;}while(x/=10); while(i--)putchar('0'+d[i]); putchar(c); } //end templatestruct fp { unsigned v; static unsigned get_mod(){return mod;} unsigned inv() const{ int tmp,a=v,b=mod,x=1,y=0; while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y); if(x<0)x+=mod; return x; } fp():v(0){} fp(ll x):v(x>=0?x%mod:mod+(x%mod)){} fp pow(ll t){fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;}return res;} fp& operator+=(const fp& x){if((v+=x.v)>=mod)v-=mod;return *this;} fp& operator-=(const fp& x){if((v+=mod-x.v)>=mod)v-=mod; return *this;} fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;} fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;} fp operator+(const fp& x)const{return fp(*this)+=x;} fp operator-(const fp& x)const{return fp(*this)-=x;} fp operator*(const fp& x)const{return fp(*this)*=x;} fp operator/(const fp& x)const{return fp(*this)/=x;} bool operator==(const fp& x)const{return v==x.v;} bool operator!=(const fp& x)const{return v!=x.v;} }; using Fp=fp<>; templatestruct factorial { vector Fact,Finv,Inv; factorial(int maxx){ Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx); Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1; unsigned mod=Fp::get_mod(); rep(i,2,maxx){ Fact[i]=Fact[i-1]*i; Inv[i]=Inv[mod%i]*(mod-mod/i); Finv[i]=Finv[i-1]*Inv[i]; } } T fact(int n,bool inv=0){if(inv)return Finv[n];else return Fact[n];} T inv(int n){return Inv[n];} T nPr(int n,int r){if(n<0||nstruct NTT{ vector rt,irt; NTT(int lg=21){ const unsigned m=T(-1).v; T prt=p; rt.resize(1<>w),ig=g.inv(); for(int i=0;i& f,bool inv=0){ int n=f.size(); if(inv){ for(int i=1;i>1;i;i>>=1)for(int j=0;j conv(vector a,vector b,bool same){ int n=a.size()+b.size()-1,m=1; while(m; using M2=fp<1051721729>; using M3=fp<1053818881>; NTT,3> N1; NTT,6> N2; NTT,7> N3; inline vector multiply(vector a,vector b,bool same=0){ int n=a.size()+b.size()-1; vector res(n); vector vals[3]; vector aa(a.size()),bb(b.size()); rep(i,0,a.size())aa[i]=a[i].v; rep(i,0,b.size())bb[i]=b[i].v; vector a1(ALL(aa)),b1(ALL(bb)),c1=N1.conv(a1,b1,same); vector a2(ALL(aa)),b2(ALL(bb)),c2=N2.conv(a2,b2,same); vector a3(ALL(aa)),b3(ALL(bb)),c3=N3.conv(a3,b3,same); for(M1 x:c1)vals[0].push_back(x.v); for(M2 x:c2)vals[1].push_back(x.v); for(M3 x:c3)vals[2].push_back(x.v); M2 r_12=175287122; M3 r_13=395182206,r_23=526909943,r_1323=461108887; Fp w1=1045430273; Fp w2=372986501; rep(i,0,n){ ll a=vals[0][i]; ll b=(vals[1][i]+M2::get_mod()-a)*r_12.v%M2::get_mod(); ll c=((vals[2][i]+M3::get_mod()-a)*r_1323.v+ (M3::get_mod()-b)*r_23.v)%M3::get_mod(); res[i]=(a+b*w1.v+c*w2.v); } return res; } factorial fact(1048576); templatestruct Poly{ vector f; Poly(){} Poly(int _n):f(_n){} Poly(vector _f){f=_f;} T& operator[](const int i){return f[i];} T eval(T x){T res,w=1; for(T v:f)res+=w*v,w*=x; return res;} int size()const{return f.size();} Poly resize(int n){Poly res=*this; res.f.resize(n); return res;} void shrink(){while(!f.empty() and f.back()==0)f.pop_back();} Poly inv()const{ assert(f[0]!=0); int n=f.size(); Poly res(1); res[0]=f[0].inv(); for(int k=1;kf.size())f.resize(g.size()); rep(i,0,g.size())f[i]+=g[i]; shrink(); return *this; } Poly& operator-=(Poly g){ if(g.size()>f.size())f.resize(g.size()); rep(i,0,g.size())f[i]-=g[i]; shrink(); return *this; } Poly& operator*=(Poly g){f=multiply(f,g.f); shrink(); return *this;} Poly& operator/=(Poly g){ if(g.size()>f.size())return *this=Poly(); reverse(ALL(f)); reverse(ALL(g.f)); int n=f.size()-g.size()+1; f.resize(n); g.f.resize(n); *this*=g.inv(); f.resize(n); reverse(ALL(f)); shrink(); return *this; } Poly& operator%=(Poly g){*this-=*this/g*g; shrink(); return *this;} Poly diff(){Poly res(f.size()-1); rep(i,0,res.size())res[i]=f[i+1]*(i+1); return res;} Poly inte(){Poly res(f.size()+1); for(int i=res.size()-1;i;i--)res[i]=f[i-1]*fact.inv(i); return res;} Poly log(){ assert(f[0]==1); int n=f.size(); Poly res=diff()*inv(); res=res.inte(); return res.resize(n); } Poly exp(){ assert(f[0]==0); int n=f.size(); Poly res(1),g(1); res[0]=g[0]=1; for(int k=1;k f(n+1); rep(i,1,n+1)f[i]=(i+1)*(i+1); Poly f1=f,f2=f; for(auto& x:f1.f)x*=I; for(auto& x:f2.f)x*=-I; Poly s=f1.exp(),t=f2.exp(); Fp c1=Fp(I*2).inv(),c2=Fp(2).inv(); rep(i,1,n+1){ Fp res=(s[i]-t[i])*c1+(s[i]+t[i])*c2; res*=fact.fact(n); put(res.v); } return 0; }