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>
int main(){
	int n,i,j,m,M=1e9+7,d[100010]={};
	long long s=1;
	scanf("%d",&n);
	for(i=2;i<=n;i++){
		m=i;
		for(j=2;j<=n;j++){
			for(;m&&m%j==0;m/=j)d[j]++;
		}
	}
	//for(i=0;i<=n;i++)printf("%d %d\n",i,d[i]);
	for(i=0;i<=n;i++)s=(s*(d[i]+1))%M;
	printf("%lld",s);
	return 0;
}