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 <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <math.h>
#define MOD 1000000007
typedef long long ll;
using namespace std;

int main(){
  ll n,ans=1;
  cin>>n;
  ll f[n+1]={};

  for(int i=2;i<=n;i++){
    ll x=i;
    for(int j=2;;j++){
      while(x%j==0){
        f[j]++;
        x/=j;
      }
      if(x==1) break;
    }
  }
  for(int i=2;i<=n;i++){
    ans=(ans*(f[i]+1))%MOD;
  }
  cout<<ans<<endl;
  return 0;
}