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>
#define acc 1000000007
int main() {
	int n, num[1000] = { 0 }, x;
	int flag = 0;
	long long ans = 1;

	scanf("%d", &n);
	for (int i = 2;i <= n;i++) {//i 割られる
		x = i;
		for (int j = 2; j <= x; j++) {
			while (x % j == 0) { //xをjでわりきれるか
				num[j - 1]++;//スタートが j=2
				x /= j;//素因数分解
			}
		}
	}
	for (int i = 1;i < 1000;i++){
		ans *= (long long)num[i] + 1;
		ans %= acc;
	}
	printf("%lld\n", ans);
	return 0;
}