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 cns (int)(1e9+7)
 
int fn(int a,int b){
	if(b<a){
		return 0;
	}
	else{
		return fn(a,b/a)+b/a;
	}
}
 
int main(){
	int N,i,j;
	long long int num=1;
	scanf("%d",&N);
	int p[N+1];
	for(i=0;i<=N;i++){
		p[i]=i;
	}
	for(i=2;i<=N;i++){
		if(p[i]!=0){
			for(j=1;i*j<=N;j++){
				p[i*j]=0;
			}
			num=(num*(fn(i,N)+1))%cns;
		}
	}
	printf("%d\n", num);
  return 0;
}