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 kthdivisor{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong(); //12
		long k = sc.nextLong(); //5
		List<Long> list = new ArrayList<>();
		list.add((long)0); // 0 1 12 
		for(long i=1; i*i<=n; i++)
			if(n%i == 0){
				list.add(i);
				if(i*i != n)
					list.add(n/i);
			}
		Collections.sort(list);
		if(k >= list.size())
			System.out.print("-1");
		else
			System.out.print(list.get((int)k));
	}
}