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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.TreeSet;

public class Main {

    public static void main(String args[]) throws IOException {
        BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
        String [] s2 = input.readLine().split(" ") ;
        long n = Long.parseLong(s2[0]);
        int k = Integer.parseInt(s2[1]);

        TreeSet<Long> list = new TreeSet();
        for (long i = 1; i * i <= n; i++) {
            if (n % i == 0) {
                list.add(i);
                list.add(n / i);
            }
        }
        System.out.println(k<=list.size() ? list.toArray()[k-1] : -1);
    }
}