Description

Input

Output

Sample Input

Sample Output

HINT

題解：顯然y>n!;

設y=n!+a;

代入原式子可以得到x=((n!)^2)/a+n!;

然後答案就是(n!)^2的因子個數了.

程式碼:

#include<iostream>
#include<cstdio>
#include<cstring>
#define P 1000000007
#define N 1000010
using namespace std;
int n,m,p[N];
long long ans(1),temp;
bool f[N];
void pre(int x){
   memset(f,1,sizeof(f));
   for (int i=2;i<=n;i++){
     if (f[i]) p[++p[0]]=i;
     for (int j=1;j<=p[0]&&p[j]*i<=n;j++){
        f[i*p[j]]=false;
        if (i%p[j]==0) break;
      }
   }
}
int main(){
   scanf("%d",&n);pre(n);
   for (int i=1;i<=p[0];i++){
      temp=0;m=n;
      while (m){temp+=m/p[i];m/=p[i];}
      temp=(temp<<1|1)%P;(ans*=temp)%=P;
   }
  cout<<ans<<endl;
}