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.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 NumberFormatException, IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		long n = sc.nextLong();
		int k = sc.nextInt();
		
		ArrayList<Long> div = new ArrayList<Long>();
		for(int i = 1; (long) i * i <= n; i++) {
			if(n % i == 0) {
				div.add((long)i);
				if((long)i * i != n)
					div.add(n / i);
			}
		}

		Collections.sort(div);
		if(k > div.size())
			System.out.println(-1);
		else
			System.out.println(div.get(k - 1));
		
		out.flush();
		out.close();
	}
	static class Scanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		
		String next() throws IOException {
			if(st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		
		String nextLine() throws IOException {
			return br.readLine();
		}
		
		int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}
		
		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}
	}
}