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.io.*;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

/**
 * Created by ReaL PC on 12/6/2016.
 */
public class AAABBB {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        String[] element = br.readLine().split(" ");
        long n = Long.parseLong(element[0]);
        int k = Integer.parseInt(element[1]);
        ArrayList<Long> arr = new ArrayList<>();
        for (long i = 1; i * i <= n; i++) {
            if (n % i == 0) {
                arr.add(i);
                if (i * i != n)
                    arr.add(n / i);
            }
        }
        Collections.sort(arr);
        if (k > arr.size())
            bw.write("-1");
        else {
            bw.write(String.valueOf(arr.get((int) (k - 1))));
            //bw.flush();
        }
        bw.flush();
    }


}