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.util.Scanner;
import java.io.*;
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
 
public class A762
{
    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 void main(String args[]) 
    {  
        FastReader in=new FastReader();
        long n=in.nextLong();
        long k=in.nextLong();
        long count=0;
        int flag=0;
        for(long i=1;i*i<=n;i++)
        {
            if(n%i==0)
                count++;
            if(i*i==n)
                flag=1;

        }
        if(flag==0)
            count*=2;
        else
            count=count*2-1;

        long maincount=0;
        int flag2=0;
        for(long i=1;i*i<=n;i++)
        {
            if(n%i==0)
                maincount++;
            if(maincount==k)
                {
                    System.out.println(i);
                    flag2=1;
                    break;
                }
            else if(count-maincount+1==k)
            {
                System.out.println(n/i);
                flag2=1;
                break;
            }
        }
        if(flag2==0)
            System.out.println(-1);
                

        
      
    } 
}