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:
// Working program with FastReader
import java.util.*;
import java.io.*;
 public class test{
    public static void main(String[] args)
    {

        int x;
        FastReader scan=new FastReader();
        long n=scan.nextLong();
        long k=scan.nextLong();
        ArrayList arr=new ArrayList();
        int sqrt=(int)Math.sqrt(n);
        //System.out.println(sqrt);
        for(x=1;x<=sqrt;x++)
        {
            if(n%x==0)
            {
                arr.add((long)x);
                long d=n/x;
                if(d!=x)
                    arr.add(d);

            }
        }

        Collections.sort(arr);
        if(k<=arr.size())
            System.out.println(arr.get((int)k-1));
        else
            System.out.println("-1");


    }
     static class FastReader
     {
         BufferedReader br;
         StringTokenizer st;

         public FastReader()
         {
             br = new BufferedReader(new
                     InputStreamReader(System.in));
         }

         String next()
         {
             while (st == null || !st.hasMoreElements())
             {
                 try
                 {
                     st = new StringTokenizer(br.readLine());
                 }
                 catch (IOException  e)
                 {
                     e.printStackTrace();
                 }
             }
             return st.nextToken();
         }

         int nextInt()
         {
             return Integer.parseInt(next());
         }

         long nextLong()
         {
             return Long.parseLong(next());
         }

         double nextDouble()
         {
             return Double.parseDouble(next());
         }

         String nextLine()
         {
             String str = "";
             try
             {
                 str = br.readLine();
             }
             catch (IOException e)
             {
                 e.printStackTrace();
             }
             return str;
         }
     }
}