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 helloWorld 
{
	public static void main(String[] args) 
	{		
		Scanner in = new Scanner(System.in);
		long n = in.nextLong();
		int m = in.nextInt();
		long ans = -1;
		ArrayList<Long> ar = new ArrayList<Long>();

		long a = (long) Math.sqrt(n);
		for(long i = 1; i <= a; i++)
			if(n % i == 0) {
				ar.add(i);
				if(i*i != n)
					ar.add(n/i);
			}
		Collections.sort(ar);
		if(m <= ar.size())
			ans = ar.get(m-1);
		
		System.out.print(ans);
		
		in.close();
	}
}