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 <cstring>
#include <cmath>
#include <limits>


using namespace std;


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

    int factors[1001];
    memset(factors, 0, sizeof(factors));

    for (int i = N; i >= 2; i--) {
        int x = i;
        while (x > 1) {
            for (int j = 2; j <=i; j++)
                if (x % j == 0) {
                    x /= j;
                    factors[j]++;
                    break;
                }
        }
    }

    long ans = 1;
    for (int i = 2; i <= N; i++) {
        if (factors[i] != 0) {
            // cout << i << ": " << factors[i] << endl;
            ans *= (factors[i] + 1);
            ans %= 1000000000 + 7;
        }
    }

    cout << ans << endl;
}