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 N = 1e5+10;
typedef long long ll;
const int mod = 1e9+7;
int a[N];
int main()
{
    int n;
    while(~scanf("%d", &n))
    {
        memset(a,0,sizeof(a));
        for(int i = 2; i <= n; i++)
        {
            int x = i;
            for(int j = 2; j <= x; j++)
                if(x%j == 0)
                    while(x%j == 0) x /= j,a[j]++;
            if(x > 1) a[x]++;
        }
        ll ans = 1;
        for(int i = 0; i < n;i++)
            if(a[i]) ans = (ans*(a[i]+1))%mod;
        cout<<ans<<endl;
    }
    return 0;
}