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:
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		long n;
		int k;
		
		Scanner scan = new Scanner(System.in);
		TreeSet<Long> ans = new TreeSet<Long>();
		
		n = scan.nextLong();
		k = scan.nextInt();
		
		for (long i = 1; i * i <= n; i++) {
			if (n % i == 0) {
				ans.add(i);
				
				if (n / i != i)
					ans.add(n/i);
			}
		}
		
		Object[] res = ans.toArray();
		
		if (k <= ans.size()) {
			System.out.println(res[k-1].toString());
		} else System.out.println(-1);
	}
}