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: Wrong Answer)

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std; 

int n;

bool isprime(int x){
  for(int i=2;i*i<=x;i++){
    if(x%i==0){
      return false;
    }
  }
  return true;
}

int main(){
  cin>>n;
  vector<long long>a(n+1,1);
  for(int i=2;i<=n;i++){
    int ii=i;
    for(int j=2;j<=ii;j++){
      if(isprime(j)){
        while(ii%j==0){
          ii=ii/j;
          a[j]++;
        }
      }
    }
  }
  long long mod=1000000007;
  long long ans=1;
  for(int i=2;i<=n;i++){
    ans*=(a[i]%mod);
  }
  cout<<ans<<endl;
}