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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Locale;
import java.util.StringTokenizer;

public class min {


    public static void main(String[] args) throws IOException {

        BufferedReader in =new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer token = new StringTokenizer(in.readLine());

        long num = Long.parseLong(token.nextToken());
        long k =  Long.parseLong(token.nextToken());

        ArrayList <Long> vec = new ArrayList<>();

        for (long i=1; i<= ((long) Math.sqrt(num)); i++){
            if(num%i == 0) {
                vec.add(i);
                if ((long) Math.ceil(Math.sqrt(num)) != i){vec.add(num / i);}
            }//if

        }//for
        Collections.sort(vec);

        if( k > vec.size()){
            System.out.println(-1);
        }//if
        else{
            System.out.println(vec.get((int) (k-1)));}

    }//main
}//class