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 Mathematical;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class KthDivisor {
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String line[]=br.readLine().split(" ");
        long n=Long.parseLong(line[0]);
        int k=Integer.parseInt(line[1]);
        ArrayList<Long> small=new ArrayList<>();
        ArrayList<Long> large=new ArrayList<>();
        for(int i=1;i<=(int)Math.sqrt(n);i++){
            if(n%i==0){
                small.add((long)i);
                if(n/i!=i)
                large.add(n/i);
            }
        }
        if(small.size()>=k){
            System.out.println(small.get(k-1));
            return;
        }
        k=k-small.size();
        if(large.size()>=k){
            System.out.println(large.get(large.size()-k));
            return;
        }
        System.out.println("-1");
    }
}