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.Scanner;
import java.util.Arrays;
import java.util.Vector;
import java.util.Collections;


public class MainTest{
	
	////////////////////////////////////////////////////////////////////////////////////////////////////
	
	public static void main(String strm[]) {
		
		Scanner scan=new Scanner(System.in);
		Vector<Long> v=new Vector<Long>();
		
		
		long n=scan.nextLong();
		int k=scan.nextInt();
				

		
		for (long i = 1; i <=Math.sqrt(n); i++)
			if(n%i==0) {
				v.add(i);
				if(i!=Math.sqrt(n) && n!=1)
					v.add(n/i); }
				
			v.sort(null);
			if(v.size()<k) { System.out.print(-1); System.exit(0);}
			
			System.out.println(v.elementAt(k-1));
			//System.out.println(v);
	}
	////////////////////////////////////////////////////////////////////////////////////////////////////
}