拯救世界

推导可得

ans=(n+1)(n+2)(n+3)(n+4)/24

于是乎打了一发py

mdTLE

然后迫不得已写了一发ntt

#include<cstdio>
#include<algorithm>
#include<iostream>
const int mod = 998244353,g=3;
const int maxn = 1001000;
typedef long long ll;
inline int pow(int a,int b,int ans=1){
    for(;b;b>>=1,a=ll(a)*a%mod)
        if(b&1)ans=ll(ans)*a%mod;
    return ans;
}
inline int inv(int x){return pow(x,mod-2);}
int wn[maxn],rev[maxn],lim;
inline void init(int len){
    *wn=lim=1;
    while(lim<len)lim<<=1;
    for(int i=1;i<lim;++i)rev[i]=rev[i>>1]>>1|(i%2*lim/2);
}
inline int reduce(int x){return x+(x>>31&mod);}
inline void fst(int*a,int type){
    for(int i=1;i<lim;++i)if(rev[i]>i)std::swap(a[rev[i]],a[i]);
    for(int mid=1;mid<lim;mid<<=1){
        const int W=pow(g,mod/mid/2);
        for(int k=1;k<mid;++k)wn[k]=ll(wn[k-1])*W%mod;
        for(int j=0;j<lim;j+=mid+mid){
            for(int*A=a+j,*B=A+mid,*w=wn;w!=wn+mid;++A,++B,++w){
                const int x=*A,y=ll(*B)**w%mod;
                *A=reduce(x+y-mod),*B=reduce(x-y);
            }
        }
    }
    if(!type){
        for(int i=0,lm=inv(lim);i<lim;++i)a[i]=ll(a[i])*lm%mod;
        std::reverse(a+1,a+lim);
    }
}
int a[maxn],b[maxn],c[maxn],d[maxn];
char buf[maxn];
int n;
inline void get(int * a){
    for(int i=0;i+1<maxn;++i)
        a[i+1]+=a[i]/10,a[i]%=10;
}
inline void div24(int*a){
    for(int i=maxn-1,res=0;~i;--i){
        res *= 10,res += a[i];
        a[i] = res / 24,res %= 24;
    }
}
int main(){
    fread(buf,1,sizeof buf,stdin);
    for(n=0;isdigit(buf[n]);++n);
    std::reverse_copy(buf,buf+n,a);
    for(int i=0;i<n;++i) b[i]=c[i]=d[i]=a[i]-=48;
    a[0]+=1,b[0]+=2,c[0]+=3,d[0]+=4;
    init(n<<1);
    fst(a,1),fst(b,1),fst(c,1),fst(d,1);
    for(int i=0;i<lim;++i)a[i]=ll(a[i])*c[i]%mod,b[i]=ll(b[i])*d[i]%mod;
    fst(a,0),fst(b,0);
    get(a),get(b);
    init(n<<2);
    fst(a,1),fst(b,1);
    for(int i=0;i<lim;++i)a[i]=ll(a[i])*b[i]%mod;
    fst(a,0),get(a),div24(a);
    for(n=maxn-1;!a[n];--n);
    for(int i=n;~i;--i)putchar(a[i]+48);
}

原文地址：https://www.cnblogs.com/skip1978/p/10346470.html