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.BufferedWriter;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.nio.ByteBuffer;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Stack;


 public class Main{
     
     
     
     public static void main(String[] args) throws IOException {
         //String IN = "C:\\Users\\ugochukwu.okeke\\Desktop\\in.file";
         //String OUT = "C:\\Users\\ugochukwu.okeke\\Desktop\\out.file";
         BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
         BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
         
         String[] in = br.readLine().split(" ");
         long n = Long.parseLong(in[0]);
         int k = Integer.parseInt(in[1]);
         ArrayList<Long> A = new ArrayList<>();
         ArrayList<Long> B = new ArrayList<>();
         for(int i=1;i<=Math.sqrt(n);i++) {
             if(n%i==0){
                 A.add(1l*i);
                 if(1l*i!=(1l*(n/i))){
                     B.add(1l*(n/i));
                 }
             }
         }
         for(int i=B.size()-1;i>=0;i--) A.add(B.get(i));
         if(k>A.size()) bw.append("-1\n");
         else bw.append(A.get(k-1)+"\n");
        bw.close();
         
     }
     
 }