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.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class A {

    public static void main(String[] args) throws IOException {
	MyScanner sc = new MyScanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	long n = sc.nextLong();
	int k = sc.nextInt();
	long x = (long) Math.sqrt(n);
	ArrayList<Long> a = new ArrayList<>();
	for (long i = 1; i <= x; i++) {
	    if (n % i == 0) {
		a.add(i);
		if (n / i != i)
		    a.add(n / i);
	    }
	}
	if (k > a.size())
	    System.out.println(-1);
	else {
	    Collections.sort(a);
	    System.out.println(a.get(k - 1));
	}
	out.flush();
	out.close();
    }

    static class MyScanner {

	BufferedReader br;
	StringTokenizer st;

	MyScanner(InputStream is) {
	    br = new BufferedReader(new InputStreamReader(is));
	}

	String next() throws IOException {
	    while (st == null || !st.hasMoreTokens())
		st = new StringTokenizer(br.readLine());
	    return st.nextToken();
	}

	int nextInt() throws IOException {
	    return Integer.parseInt(next());
	}

	long nextLong() throws IOException {
	    return Long.parseLong(next());
	}

	boolean ready() throws IOException {
	    return br.ready();
	}
    }
}