Problem:
Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<cstdio>
using namespace std;
int main(){
  int n,b;
  long ans=1,a[1001];
  for(int i=0;i<=1000;i++)
    a[i]=1;
  scanf("%d",&n);
  for(int i=1;i<=n;i++){
    b=i;
    for(int j=2;j<=n;j++){
      while(b%j==0){
        a[j]++;
        b/=j;
      }
      if(b==1)
        break;
    }
  }
  for(int i=2;i<=n;i++){
    ans*=a[i];
    ans%=1000000007;
  }
  printf("%ld\n",ans);
}