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 Task762{
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    long n = in.nextLong();
    int k = in.nextInt();
    Set<Long> set = new HashSet<Long>();
    for (int i = 1; i <= Math.sqrt(n); ++i)
    {
      if (n % i == 0)
      {
          set.add((long)i);
          if(n/i != 0)
            set.add((long)n/i);
      }
    }
    Long[] array = set.toArray(new Long[0]);
    Arrays.sort(array);
    if(array.length >= k)
      System.out.println(array[k-1]);
    else
      System.out.println("-1");
  }
}