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.ArrayList;
import java.util.Collections;

public class A {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] input = br.readLine().split(" ");
		long n = Long.parseLong(input[0]);
		int k = Integer.parseInt(input[1]);
		long divisor = -1;
		ArrayList<Long> divisors = new ArrayList<>();
		for (long i = 1; i*i <= n; i++) {
			if (n % i == 0){
				divisors.add(i);
				if ( i* i < n) divisors.add(n / i);
			}
		}
		Collections.sort(divisors);
		if (divisors.size() < k) {
			divisor = -1;
		} else {
			divisor = divisors.get(k-1);
		}
		System.out.println(divisor);
	}
}