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 int mod = 1e9 + 7;

bool primes[1007];
int cnt[1007];

void sieve(int n)
{
    for (int i = 2; i <= n; i++) {
        if (primes[i]) continue;
        for (int j = i+i; j <= n; j += i) {
            primes[j] = 1;

            int tmp = j;
            while (tmp % i == 0) cnt[i]++, tmp /= i;
        }
        cnt[i]++;
    }
}

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

    sieve(n);

    ll nod = 1;
    for (int i = 2; i <= n; i++) {
        if (!primes[i]) nod = (nod * (cnt[i] + 1)) % mod;
    }

    cout << nod << endl;
}