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:
//I AM THE CREED
/* package codechef; // don't place package name! */
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;
 
public class HelloWorld{
    public static void main(String[] args) throws IOException 
    { 
  
        Scanner input = new Scanner(System.in);
        while(input.hasNext()){
            long ct=0;
            long n=input.nextLong();
            int k=input.nextInt();
            boolean found=false;
            long num=-1;
            for(int i=1;i<=(int)(Math.sqrt(n));i++){
                if(n%(long)(i)==0){
                    ct++;
                    if(ct==k){
                        found=true;
                        num=(long)(i);
                        break;
                    }
                }
            }
            if(found){
                System.out.println(num);
                continue;
            }
            for(int i=(int)(Math.sqrt(n));i>=1;i--){
                long t=(long)(i);
                if(t*t==n){
                    continue;
                }
                if(n%(long)(i)==0){
                    ct++;
                    if(ct==k){
                        found=true;
                        num=n/(long)(i);
                        break;
                    }
                }
            }
            System.out.println(num);
        }
    }

}