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 demo {

	public static void main(String[] args)  throws java.lang.Exception {
		
		Scanner sc = new Scanner(System.in);
		Long n = sc.nextLong();
		int k = sc.nextInt();
		sc.close();
		Vector<Long> v=new Vector<>(); 
		for(Long i=(long)1 ;i<=(int)Math.sqrt(n);i++)
		{

			if(n%i==0){
				if(i==(n/i)){
					v.add(i);
				}else{
					v.add(i);
					v.add((n/i));
				}
			}
		}
		Collections.sort(v);
		
		if(v.size() >=k){
			System.out.print(v.get(k-1));
		}
		else{
			System.out.print(-1);
		}
		
	}
}