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.*;
import java.io.PrintWriter;

public class A762 implements Runnable {
	private Scanner in = new Scanner(System.in);
	private PrintWriter out = new PrintWriter(System.out); 

	private long n;
	private int k;

	public static void main(String[] args) {
		new Thread(new A762()).start();
	}

	private void read() {
		n = in.nextLong();
		k = in.nextInt();
		
	}

	private void solve() {

		boolean bool = false;
		
		int s = (int) Math.sqrt(n);
		int count = 0;
		ArrayList<Long> a = new ArrayList<Long>();

		for(int i = 1; i <= s; i++) {
			if(n % i == 0) {
				a.add((long)i);

				if(n/i != i) {

					a.add(n/i);
				
				}
			}
		}

		Collections.sort(a);
		
		if(a.size() >= k) {
			out.println(a.get(k-1));
		} else {
			out.println("-1");
		}




	}

	private void write() {

	}

	public void run() {
		read();
		solve();
		write();
		out.close();
	} 
}