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.*;
import java.util.*;
public class Problem1Watermelon {
 
    public static void isprime(long x, Set s)
    {
            for (long i = 1; i <= Math.sqrt(x); i++) {
                if (x%i==0) {
                    s.add(i);
                    s.add(x/i);
                }
            }
    }
   
    public static void main(String[] args)  {
        Scanner in=new Scanner(System.in);
        Set <Long> s=new TreeSet<>();
        long n=in.nextLong(),k=in.nextLong();
        Object arr[];
        isprime(n,s);
        Iterator it= s.iterator();
        arr=s.toArray();
        if (arr.length>=k) {
            System.out.println(arr[(int)k-1]);
        }
        else{
            System.out.println("-1");
        }  
    }
}