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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
const int MAX_LIM = 1e3;
const long long MOD = 1e9 + 7;
typedef long long ll;

int fact[MAX_LIM];

void factoring(int num){
	int x = 2;
	while(num >= x*x){
		if(num%x == 0) num /= x;
		else x++;
	}
	fact[num]++;
}

int main(){
	ll n;
	cin >> n;
	ll ans = 1;
	
	if(n == 1) {
		cout << 1 << endl;
		return 0;
	}
	
	for(int i=2; i<=n; i++) factoring(i);
	
	for(int i=2; i<=n; i++){
		if(fact[i] == 0) continue;
		else ans *= fact[i] + 1;
		ans %= MOD;
	}
	cout << ans << endl;
  
  return 0;
}