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.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;

public class Main
{
    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; 
        } 
    }

     public static long[] randomize(long arr[])
    {
        Random rand = new Random();
for (int i = 0; i < arr.length; ++i) {
   int index = rand.nextInt(arr.length - i);
   long tmp = arr[arr.length - 1 - i];
   arr[arr.length - 1 - i] = arr[index];
   arr[index] = tmp;
}

return arr;
    } 
    static long mod = 1000000007;

  
    public static void main (String[] args) throws java.lang.Exception
    {
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        
       long n = sc.nextLong();
       long k = sc.nextLong();
       List<Long> l =new ArrayList<>();
       for(long i=1;i<=(long)Math.sqrt(n);i++)
       {
            if(n%i==0)
            {
                l.add(i);
                if(i!=n/i)
                l.add(n/i);

            }
       }
    //  System.out.println(l);
       if(k>(long)l.size())
        System.out.println(-1);
        else
            {
                Collections.sort(l);
          //      System.out.println(l);
                System.out.println(l.get((int)k-1));
            }
    }
    
    
    
    
}