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 s = new Scanner(System.in);
		long n=s.nextLong();
		int k=s.nextInt();
		ArrayList<Long> ans = new ArrayList<Long>();
		int insert=0;
		for(long i=1;i<=Math.sqrt(n);i++){
			if(n%i==0){
				if(i*i==n){
					ans.add(insert,i);
				}
				else{
					ans.add(insert,n/i);
					ans.add(insert,i);
				}
				insert++;
			}
		}
		if(k>ans.size()){
			System.out.print("-1");
		}
		else{
			System.out.print(ans.get(k-1));
		}
	}
}