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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;



public class Problem1 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		long n = in.nextLong();
		int k = in.nextInt();
		int sqrt = (int) (Math.sqrt(n));
		ArrayList<Long> div = new ArrayList<>();
		if(k > 2*sqrt)
		{
			out.println(-1);
			out.close();
			return;
		}
		
		for(int i = 1; i <= sqrt; ++i)
		{
			if(n%i == 0)
			{
				div.add((long) i);
				if(i != n/i)
				{
					div.add((n/i));
				}
			}
		}
		if(div.size() < k)
		{
			out.println(-1);
			out.close();
			return;
		}
		
		Collections.sort(div);
		out.println(div.get(k-1));
		out.close();
	}
	
	public static int getAns(int[] arr, int k)
	{
		Arrays.sort(arr);
		return arr[k-1];
	}
	

	

	
	
	static class InputReader {
	    public BufferedReader reader;
	    public StringTokenizer tokenizer;

	    public InputReader(InputStream stream) {
	        reader = new BufferedReader(new InputStreamReader(stream), 32768);
	        tokenizer = null;
	    }

	    public String next() {
	        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
	            try {
	                tokenizer = new StringTokenizer(reader.readLine());
	            } catch (IOException e) {
	                throw new RuntimeException(e);
	            }
	        }
	        return tokenizer.nextToken();
	    }
 
	    public int nextInt() {
	        return Integer.parseInt(next());
	    }
	    
	    public long nextLong()
	    {
	    	return Long.parseLong(next());
	    }

	}


}