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;

typedef long long ll;
const ll MOD = 1e9 + 7;
const ll inf = 1LL<<60;
const double eps = 1e-9;

map< int, int > ret;

map< int, int > prime_factor(int n) {
    for(int i = 2; i * i <= n; i++) {
        while(n % i == 0) {
            ret[i]++;
            n /= i;
        }
  }
  if (n != 1) ret[n]++;
  return ret;
}
int main()
{
    int n;
    cin >> n;
    ll ans = 1;
    for (int i = 2; i <= n; i++) {
        prime_factor(i);
    }
    for (auto p : ret) {
        (ans *= (p.second + 1)) %= MOD;
    }
    cout << ans << endl;
    return 0;
}