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 p3{
  public static void main(String[] args) {
    Scanner in=new Scanner(System.in);
    long n=in.nextLong();
    long k=in.nextLong();
    TreeSet<Long> arr=new TreeSet<>();
    Iterator<Long> it=arr.iterator();
    int p=0;
    //if(n!=1)
      for(long i=1;i<=Math.sqrt(n);i++){
        if(n%i==0){arr.add(i);arr.add(n/i);}
      }
      //else{arr.add((long)1);}
    if(k>arr.size()){System.out.println(-1);}
    else{
      //Collections.sort(arr);
      //System.out.println(arr.get((int)k-1));
      while(k!=arr.size()){
        arr.pollLast();
      }System.out.println(arr.pollLast());

    }
    //for(long i=0;i<arr.size();i++){System.out.print(arr.get((int)i)+" ");}
  }
}