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,k,c[100010]={};
  long long ans=1,M=1e9+7;
  scanf("%d",&n);
  for(i=1;i<=n;i++){
    k=i;
    for(j=2;j<=i;j++){
      while(k%j==0){
	c[j]++;
	k/=j;
      }
    }
  }
  //for(i=0;i<=n;i++)printf("%d\n",c[i+1]);
  for(i=1;i<=n;i++)ans=(ans*(c[i]+1))%M;
  printf("%lld\n",ans);
  return 0;
}