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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = 1000;sc.nextInt();
        boolean [] b = new boolean [1001];
        ArrayList<Integer> prime = new ArrayList<Integer>();
        prime.add(2);
        for(int i=3; i<=1000; i+=2){
            if(b[i]==false){
                prime.add(i);
                int k=3;
                while(i*k<=1000){
                    b[i*k]=true;
                    k+=2;
                }
            }
        }
        int s = prime.size();
        long [] PNum = new long [s];
        for(int i=0; i<s; i++){
            int P = prime.get(i);
            for(int j=1; j<=N; j++){
                int tmp=j;
                while(tmp%P==0){
                    PNum[i]++;
                    tmp/=P;
                }
            }
        }
        long ans=1;
        long mod=1000000007;
        for(int i=0; i<s; i++){
            ans*=(PNum[i]+1);
            ans%=mod;
        }
        System.out.println(ans);
    }
}