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: Wrong Answer)

#include<stdio.h>
#include<math.h>
#define T 1000000007
int main() {
	long long int n,ans=1,i,j,x,a;
	long long int f[1010];
	scanf("%lld",&n);
	for(i=2; i<=n; i++) {
		x=i;
		for(j=2; j<=n; j++) {
			if(j>x)
				break;
			a=0;
			while(x%j==0) {
				x/=j;
				a++;
			}
			f[j]+=a;
		}
	}
	for(i=2; i<=n; i++) {
		f[i]++;
		ans=(ans*f[i])%T;
	}
	printf("%lld\n",ans);
	return 0;
}