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 N = 1100;
const int mod = 1e9+7;

int prime[N];
vector <int> lista;
long long qtd[N];

int main() {
	int n;
	scanf("%d", &n);

	//map <int, int> mp;

	for (int i = 2; i <= n; ++i) {
		if(prime[i]==0) {
			lista.push_back(i);
			for (int j = 2*i; j <= n; j+=i) {
				prime[j] = 1;
			}
		}
	}

	for (int i = 1; i <= n; ++i) {
		int at = i;
		for (int j = 0; j < lista.size(); ++j) {
			if (at % lista[j] == 0) {
				while(at % lista[j] == 0) {
					at /= lista[j];
					qtd[j]++;
				}
			}
		}
	}

	long long ans = 1;
	for (int i = 0; i < lista.size(); ++i) {
		ans = (ans * 1ll * (qtd[i]+1)) % mod;
	}
	printf("%lld\n", ans);
}