#include #include #include #include #include #include #include #include #include #include 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('0'); else{ if(x<0) std::putchar('-'),x*=-1; int d[20],i=0; while(x)d[i++]=x%10,x/=10; while(i--) std::putchar('0'+d[i]); } putchar(c); } constexpr long long p[3]={998244353,924844033,897581057}; constexpr long long g[3]={3,5,3}; inline long long ADD(long long a,long long b,int id) { return a+b>=p[id]?a+b-p[id]:a+b; } inline int SUB(int a,int b,int id) { return a-b<0?a-b+p[id]:a-b; } int deg(std::vector a){ int ret=a.size()-1; while (ret>=0 && a[ret]==0) --ret; return ret; } std::vector trim(std::vector a,int n) { int asize=a.size(); a.resize(n); for (int i=asize;i norm(std::vector a) { while (a.size()>1 && a.back()==0) a.pop_back(); return a; } //f->fx^(shift) std::vector shift(std::vector &a,int shift) { std::vector b(std::max(0,(int)a.size()+shift),0); for (int i=0;i<(int)b.size();++i) b[i]=(0<=i-shift&&i-shift<(int)a.size())?a[i-shift]:0; return b; } inline long long pow_mod(long long a,long long n,int id) { long long ret=1; for (;n>0;n>>=1,a=a*a%p[id]) if(n%2==1) ret=ret*a%p[id]; return ret; } inline int inv(int a,int id) { a%=p[id]; if (a<0) a+=p[id]; int u=p[id]; int v=a; int s=0; int t=1; // sa=u // ta=v while (v!=0) { int q=u/v; s-=q*t;u-=q*v; std::swap(s,t); std::swap(u,v); } assert((long long)a*(s+p[id])%p[id]==1); return s>=0?s:s+p[id]; } std::vector monic(std::vector a,int id) { if (deg(a)==-1) return a; a.resize(deg(a)+1); long long coe=inv(a[a.size()-1],id); for (int i=0;i<(int)a.size();++i) { a[i]=(int)(coe*a[i]%p[id]); } return a; } std::vector add(std::vector a,std::vector b,int id) { int n=std::max(a.size(),b.size()); a.resize(n);b.resize(n); for (int i=0;i subtract(std::vector a,std::vector b,int id) { int n=std::max(a.size(),b.size()); a.resize(n);b.resize(n); for (int i=0;i mul_naive(std::vector a,std::vector b,int id) { std::vector ret(a.size()+b.size()-1,0); for (int i=0;i<(int)a.size();++i) { for (int j=0;j<(int)b.size();++j) { ret[i+j]=(int)((ret[i+j]+1LL*a[i]*b[j])%p[id]); } } ret=norm(ret); return ret; } void fft_(int n,int g,int stride,std::vector &from,std::vector &to,bool flag,int id){ if (n==1) { if (flag) for (int i=0;i &from,std::vector &to,bool flag,int id){ int w=pow_mod(g,(p[id]-1)/n,id); long long w1,w2,w3; int i,src,n0,n1,n2,n3,A,B,C,D,apc,amc,bpd,jbmd; while (n>2) { n0=0; n1=n/4; n2=n1+n1; n3=n1+n2; w1=1; for (i=0;ito.size()) std::swap(from,to); } std::vector tmp_fft(1<<20); void fft(std::vector &a,int g,int id) { fft4_(a.size(),g,pow_mod(g,(p[id]-1)/4*3,id),1,a,tmp_fft,false,id); } // (sx^p+u)(tx^p+v) // =stx^(2p)+(sv+ut)x^p+uv // =stx^(2p)+((s+u)(t+v)-(st-uv))x^p+uv void mul_karatsuba(int a[],int b[],int c[],int res[],int n,int id) { if (n<=8) { for (int i=0;i<2*n;++i) res[i]=0; for (int i=0;i mul_fft(std::vector a,std::vector b,int id) { int n=1; int need=a.size()+b.size()-1; while (n karatsuba(std::vector a,std::vector b,int id) { int need=std::max(a.size(),b.size()); int n=1; while (n a_=trim(a,n); std::vector b_=trim(b,n); std::vector c(4*n); std::vector res(4*n); mul_karatsuba(a_.data(),b_.data(),c.data(),res.data(),n,id); res.resize(a.size()+b.size()-1); return res; } std::vector mul(std::vector a,std::vector b,int id) { if (std::max(a.size(),b.size())<=64) { return karatsuba(a,b,id); } else { std::vector ret=mul_fft(a,b,id); ret=norm(ret); return ret; } } std::vector mul(std::vector a,std::vector b,long long mod) { int n=3; std::vector f[n]; for (int i=0;i mul(std::vector a,int b,int id) { int n=a.size(); std::vector c(n); for (int i=0;i>> mul(std::vector>> a,std::vector>> b,int id) { std::vector>> ret(a.size(),std::vector>(b[0].size(),std::vector())); for (int i=0;i<(int)a.size();++i) { for (int j=0;j<(int)b[i].size();++j) { for (int k=0;k<(int)a[i].size();++k) { ret[i][j]=add(ret[i][j],mul(a[i][k],b[k][j],id),id); } } } return ret; } // f <- -f(fh-1)+f std::vector inv(std::vector h,int id) { int n=h.size(); std::vector f={inv(h[0],id)}; long long root=g[id]; long long iroot=inv(g[id],id); for (int len=1;len f_fft=trim(f,2*len); std::vector h_fft=trim(h,2*len); fft(f_fft,root,id); fft(h_fft,root,id); long long isize=inv(2*len,id); for (int i=0;i<2*len;++i) h_fft[i]=(int)(1LL*h_fft[i]*f_fft[i]%p[id]*isize%p[id]); fft(h_fft,iroot,id); for (int i=0;i divide(std::vector a,std::vector b,int id) { a=norm(a); b=norm(b); if (a.size() ret(1,0); return ret; } std::reverse(a.begin(),a.end()); std::reverse(b.begin(),b.end()); int n=a.size()-b.size()+1; a.resize(n); b.resize(n); a=mul(a,inv(b,id),id); a.resize(n); std::reverse(a.begin(),a.end()); return a; } std::vector mod(std::vector a,std::vector b,int id) { return subtract(a,mul(b,divide(a,b,id),id),id); } int main() { long long mod=(long long)1e9+7; int n=get()+1; int m=n; //int m=get(); std::vector a(n); std::vector b(m); for (int i=0;i