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;

/**
 * Created by for on 2017-01-25.
 */
public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);


        long n = sc.nextLong();
        int k = sc.nextInt();


        ArrayList<Long> list = new ArrayList<>();

        long cnt=0;
        for(long i=1; i<=Math.sqrt(n); i++) {
            if(n%i == 0) {
                if(n/i == i) {
                    list.add(i);
                } else {
                    list.add(i);
                    list.add(n/i);
                }
            }
        }
        Collections.sort(list);

        if(list.size()-1 >= (k-1)) {
            System.out.println(list.get(k-1));
        } else {
            System.out.println(-1);
        }
    }
}