Problem: You are given two integers n and k. Find k-th smallest divisor of n, or report that it doesn't exist.

Divisor of n is any such natural number, that n can be divided by it without remainder.

Input

The first line contains two integers n and k (1 ≤ n ≤ 1015, 1 ≤ k ≤ 109).

Output

If n has less than k divisors, output -1.

Otherwise, output the k-th smallest divisor of n.

Examples

Input

4 2


Output

2


Input

5 3


Output

-1


Input

12 5


Output

6

Note

In the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.

In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1.

Solution (in JAVA):

Solution:

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s=new Scanner(System.in);
		long n=s.nextLong();int k=s.nextInt();
		ArrayList<Long> ar=new ArrayList<>();
		for(long i=1;i<=Math.sqrt(n);i++){
			if(n%i==0){
				if(i*i==n)ar.add(i);
				else
				{ar.add(i);ar.add(n/i);}
					
			}
			
		}
		Collections.sort(ar);
		if(k>ar.size())System.out.println(-1);
		else
			System.out.println(ar.get(k-1));
		
		
	}

}