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 codechef; // 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 Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
	    long k = sc.nextLong();
		
	    Set<Long> set = new TreeSet<Long>();
	    
		
		for(long i=1;i<=Math.sqrt(n);i++){
			if(n%i==0 && i*i!=n){
				set.add(i);
				set.add(n/i);
			}
			if(n%i==0 && i*i==n){
				set.add(i);
			}
		}
		
		int j=0,flag=0;
		for(Long x: set){
            j++;
			if(j==k){
				System.out.println(x);
				flag=1;
				break;
			}
		}
		if(flag==0)
		    System.out.println("-1");
			
	}
}