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 <bits/stdc++.h>
using namespace std;

#define int long long

#define inf (int)1000000007

#define rep(i, n) for(int i = 0; i < (n); i++)
#define trep(i, n) for(int i = 0; i <= (n); i++)
#define rrep(i, n) for(int i = (n) - 1; i >= 0; i--)
#define trrep(i, n) for(int i = (n); i >= 0; i--)

bool u[1111];

int count(int x, int n) {
  if(x % n) {
    return 0;
  }
  return count(x / n, n) + 1;
}

signed main() {
  int n;
  cin >> n;
  trep(i, n) {
    u[i] = true;
  }
  int ans = 1;
  for(int i = 2; i <= n; i++) {
    if(u[i]) {
      int now = 0;
      for(int j = i; j <= n; j += i) {
        now += count(j, i);
        u[i] = false;
      }
      ans = (ans * (now + 1)) % 1000000007;
    }
  }
  cout << ans << endl;
}