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>
#include<string.h>
#include<stdlib.h>
#include<math.h>
#define PI 3.141592653589793
#define MOD 1000000007

int main(){
	int n;
	scanf("%d", &n);
	int yak[1001];
	for(int i=0; i<1001; i++){
		yak[i] = 1;
	}

	int temp;
	for(int i=2; i<=n; i++){
		temp = i;
		for(int j=2; temp != 1; j++){
			if(temp%j == 0){
				while(temp%j == 0){
					yak[j]++;
					temp = temp/j;
				}
			}
		}
	}
	long int answer=1;
	for(int i=0; i<1001; i++){
		answer =(long int) answer*yak[i];
		answer = answer%MOD;
	}
	printf("%ld\n", answer);

	return 0;
}