p5349 幂

分析

https://www.cnblogs.com/cjyyb/p/10822490.html

代码

#include<bits/stdc++.h>
using namespace std;
#define int long long
const int g = ;
const int N = 2e5;
const int G = ;
const int mod = ;
int f[],a[],b[],fac[],inv[],val,A[],R,r[];
inline int pw(int x,int p){int res=;while(p){if(p&)res=res*x%mod;x=x*x%mod;p>>=;}return res;}
inline void ntt(int a[],int opt,int n){
    int i,j,k,inv=pw(n,mod-),now,wn,w,p,q;
    for(i=;i<n;i++)if(i<r[i])swap(a[i],a[r[i]]);
    for(i=;i<n;i<<=){
      now=(opt==?g:G),wn=pw(now,(mod-)/(i<<));
      for(j=;j<n;j+=(i<<))
        for(k=,w=;k<i;k++,w=w*wn%mod)
          p=a[j+k],q=a[i+j+k]*w%mod,a[j+k]=(p+q)%mod,a[i+j+k]=(p-q+mod)%mod;
    }
    if(opt==-)for(i=;i<n;i++)a[i]=a[i]*inv%mod;
}
inline void go_to_work(int le,int ri){
    if(le==ri)return;
    int i,j,k,n,m=ri-le,len=,mid=(le+ri)>>;
    go_to_work(le,mid);for(n=;n<=(m+)*;n<<=)len++;
    for(i=;i<n;i++)r[i]=((r[i>>]>>)|((i&)<<(len-)));
    for(i=;i<n;i++)a[i]=b[i]=;for(i=;i<=mid-le;i++)a[i]=f[i+le];
    for(i=;i<=m;i++)b[i]=val*inv[i]%mod;ntt(a,,n),ntt(b,,n);
    for(i=;i<n;i++)a[i]=a[i]*b[i]%mod;ntt(a,-,n);
    for(i=mid+;i<=ri;i++)f[i]=(f[i]+a[i-le])%mod;
    go_to_work(mid+,ri);return;

}
signed main(){
    int n,i,j,k,Ans=;
    scanf("%lld%lld",&n,&R);
    f[]=pw((-R+mod)%mod,mod-);
    for(i=;i<=n;i++)scanf("%lld",&A[i]);
    fac[]=;for(i=;i<=N;i++)fac[i]=fac[i-]*i%mod;
    inv[N]=pw(fac[N],mod-);for(i=N-;i>=;i--)inv[i]=inv[i+]*(i+)%mod;
    val=R*pw((-R+mod)%mod,mod-)%mod;go_to_work(,n);
    for(i=;i<=n;i++)Ans=(Ans+f[i]*A[i]%mod*fac[i]%mod)%mod;
    printf("%lld\n",Ans);return ;
}