COGS 2259 异化多肽——生成函数+多项式求逆

题目：http://cogs.pro:8080/cogs/problem/problem.php?pid=2259

详见：https://www.cnblogs.com/Zinn/p/10054569.html

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
using namespace std;
const int N=1e5+,M=(<<)+,mod=,g=;
int n,a[M],b[M],A[M],len,r[M],c[M];
int rdn()
{
  int ret=;bool fx=;char ch=getchar();
  while(ch>''||ch<''){if(ch=='-')fx=;ch=getchar();}
  while(ch>=''&&ch<='') ret=ret*+ch-'',ch=getchar();
  return fx?ret:-ret;
}
void upd(int &x){x>=mod?x-=mod:;}
int pw(int x,int k)
{int ret=;while(k){if(k&)ret=(ll)ret*x%mod;x=(ll)x*x%mod;k>>=;}return ret;}
void ntt(int *a,bool fx)
{
  for(int i=;i<len;i++)
    if(i<r[i])swap(a[i],a[r[i]]);
  for(int R=;R<=len;R<<=)
    {
      int wn=pw( g,fx?(mod-)-(mod-)/R:(mod-)/R );
      for(int i=,m=R>>;i<len;i+=R)
    for(int j=,w=;j<m;j++,w=(ll)w*wn%mod)
      {
        int x=a[i+j], y=(ll)w*a[i+m+j]%mod;
        a[i+j]=x+y; upd(a[i+j]);
        a[i+m+j]=x+mod-y; upd(a[i+m+j]);
      }
    }
  if(!fx)return ; int inv=pw(len,mod-);
  for(int i=;i<len;i++)a[i]=(ll)a[i]*inv%mod;
}
void getinv(int n,int *a,int *b)
{
  if(n==){b[]=pw(a[],mod-);return;}
  getinv(n+>>,a,b);
  for(len=;len<n<<;len<<=);
  for(int i=;i<len;i++)r[i]=(r[i>>]>>)+((i&)?len>>:);
  for(int i=;i<n;i++)A[i]=a[i]; for(int i=n;i<len;i++)A[i]=;
  ntt(A,); ntt(b,);
  for(int i=;i<len;i++)b[i]=(-(ll)A[i]*b[i])%mod*b[i]%mod+mod,upd(b[i]);
  ntt(b,);
  for(int i=n;i<len;i++)b[i]=;
}
int main()
{
  freopen("polypeptide.in","r",stdin);
  freopen("polypeptide.out","w",stdout);
  n=rdn();int m;m=rdn();
  for(int i=,d;i<=m;i++)
    {
      d=rdn();
      a[d]+=mod-,upd(a[d]);
    }
  a[]++; upd(a[]);
  getinv(n+,a,b);
  printf("%d\n",b[n]);
  return ;
}