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 Main{
	public static void main(String args[]){
		Scanner sc=new Scanner(System.in);
		ArrayList<Long> obj=new ArrayList();
		long a=sc.nextLong();
		int b=sc.nextInt();
		for(long i=1 ; i<Math.sqrt(a) ; i++){
			if(a%i==0){
				obj.add(i);
				obj.add(a/i);
			}
		}
		if(a%Math.sqrt(a)==0)
			obj.add((long)Math.sqrt(a));
		if(obj.size()<b){
			System.out.println("-1");
			return;
		}
		Collections.sort(obj);
		System.out.print(obj.get(b-1));
	}
}