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 //do not write package name here */

import java.util.*;
import java.lang.*;
import java.io.*;
public class kd {

     public static void main(String[] args) 
    {       // TODO Auto-generated method stub
   Scanner sc=new Scanner(System.in);
    long n=sc.nextLong();
    int k=sc.nextInt();
    TreeSet<Long> ts=new TreeSet<Long>();
 

    for(long i=1;i<=(long)Math.sqrt(n);i++){
         if(n%i==0 ){
          ts.add(i);
          ts.add(n/i);
         }
    }
   ArrayList<Long> arr=new ArrayList<Long>(ts);
    //System.out.println(arr.size());
    if(k>arr.size()){
        System.out.println(-1);
    }else{

      System.out.println(arr.get(k-1));
    }


    
}
    
    

}