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;
const int mod = 1e9+7;
int n, a[1005], p[1005], c[1005], m;
long long ans = 1;
void siftp(int maxn) {
    a[0] = a[1] = 1;
    for (int i = 2; i < maxn; i++) {
        if (!a[i]) p[m++] = i;
        for (int j = 0; j < m; j++) {
            if (i * p[j] >= maxn) break;
            a[i*p[j]] = 1;
            if (i % p[j] == 0) break;
        }
    }
}
void handle(int x) {
    for (int i = 0; i < m && x > 1; i++) {
        while (x % p[i] == 0) {
            c[i] += 1;
            x /= p[i];
        }
    }
}
int main() {
    siftp(1005);
    scanf("%d", &n);
    for (int i = 2; i <= n; i++)
        handle(i);
    for (int i = 0; i < m; i++)
        ans = ans * (c[i] + 1) % mod;
    cout << ans << endl;
    return 0;
}