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){
		// get numbers
		Scanner sc = new Scanner(System.in);     
        int N = sc.nextInt();
        int x = 1, y = 0, z = 0, ans = 0;

        for (int i = 2; i < N; i++) {
            for (int j = 2; j <= i; j++) {
                y = i;
                z = 0;
                while (y > j) {
                    if (y % j == 0) {
                        y = y / j;
                        z++;
                    } else {
                        y = 0;
                    }
                }
                x = x * (z + 1);
            }
            ans += x;
            x = 1;
        }
        ans += N;

        // output
        System.out.println(ans);
        sc.close();
	}
}