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.*;
public class MyClass {
    public static void main(String args[]) {
      Scanner sc=new Scanner(System.in);
      long n=sc.nextLong();
      int k=sc.nextInt();
    List<Long> v1 = new ArrayList<>(); 
    List <Long> v2 = new ArrayList<>(); 
    for( long i = 1 ; i <= Math.sqrt( n ); i++ ) 
    { 
        if ( n % i == 0 )  
        { 
            v1.add ( i ); 
              
            if ( i != Math.sqrt ( n ) ) 
                v2.add ( n / i ); 
        } 
    } 
    Collections.reverse(v2); 
      
    if ( k > (v1.size() + v2.size())) 
        System.out.print("-1"); 
      
    else
    { 
        if(k <= v1.size()) 
            System.out.print(v1.get(k - 1)); 
        else
            System.out.print(v2.get(k-v1.size() - 1)); 
    } 
 
  
      
    }
}