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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
typedef long long ll;
#define MOD 1000000007
int main() {
	int n, num[1000] = {0}, x;
	ll ans = 1;
	scanf("%d", &n);
	for (int i = 2; i <= n; i++) {
		x = i;
		for (int j = 2; j <= x; j++) {
			while (x % j == 0) {
				num[j - 1]++;
				x /= j;
			}
		}
	}
	for (int i = 1; i < 1000; i++) {
		ans *= num[i] + 1;
		ans %= MOD;
	}
	printf("%lld\n", ans);
	return 0;
}