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<iostream>
#include<algorithm>
#include<math.h>
#include<cstdio>
#include<ctype.h>
#include<stdio.h>
#include<set>
#include<vector>
#include<map>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<numeric>
#include<string>
typedef long long ll;
using namespace std;

ll gcd(ll a, ll b){
if(a<b){return gcd(b,a);}
else if(a%b){return gcd(b,a%b);}
else{return b;}
}
ll prime(ll x) {
	ll i;
	if (x < 2)return 0;
	else if (x == 2) return 1;
	if (x % 2 == 0) return 0;
	for (i = 3; i*i <= x; i += 2) {
		if (x%i == 0) return 0;
	}
	return 1;
}
ll MOD = 1e9+7;
ll cnt[1010];
ll divide(ll m )
{
	while (m != 1) {
		for (ll i = 2; ; i++)
			if (m % i == 0){
				m /= i;
				cnt[i]++;
              	break;
			}
	}   
}
int main(){
  ll N;
  cin>>N;
  ll ans=1;
    for (ll i = 1; i <= N; i++){
		divide(i);
	}
  	for (ll i = 2; i <= N; i++){
		if (cnt[i]){
			ans *= (cnt[i] + 1);
			ans %= MOD;
		}
	}
 cout << ans << endl;
}