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 <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(), (x).end()
typedef long long ll;
static const int INF (1<<30);
static const int mod = 1e9+7;
ll cnt[1005];

int main() {
  int N; cin >> N;

  if (N == 1) {
    cout << 1 << endl;
    return 0;
  }

  for (int i = 2; i <= N; i++) {
    int x = i;
    int div = 2;

    while (x > 1) {
      if (x % div == 0) {
        cnt[div]++;
        x /= div;
      } else {
        div++;
      }
    }

  }


  ll ans = 1LL;
  for (int i = 1; i <= N; i++) {
    if (cnt[i] == 0LL) continue;

    ans *= cnt[i] + 1LL;
    ans %= mod;
  }

  cout << ans << endl;

  return 0;
}