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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    Task solver = new Task();
    solver.solve(1, in, out);
    out.close();
  }

  static class Task {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
      long n = in.nextLong();
      int k = in.nextInt();
      out.println(f1(n, k));
    }

    long f1(long n, int k) {
      List<Long> first = new ArrayList<>();
      List<Long> second = new ArrayList<>();
      for (long i = 1; i * i <= n; i++) {
        if (n % i == 0) {
          first.add(i);
          if (i * i != n) {
            second.add(n / i);
          }
        }
      }
      int s = first.size() + second.size();
      if (s < k) {
        return -1;
      } else {
        if (first.size() >= k) {
          return (first.get(k - 1));
        } else {
          return (second.get(second.size() - k + first.size()));
        }
      }
    }

  }

  static class InputReader {
    BufferedReader br;
    StringTokenizer in;

    public InputReader(String fileName) {
      try {
        br = new BufferedReader(new FileReader(fileName));
      } catch (IOException e) {
        throw new RuntimeException(e);
      }
    }

    public InputReader(InputStream inputStream) {
      br = new BufferedReader(new InputStreamReader(inputStream));
    }

    boolean hasMoreTokens() {
      while (in == null || !in.hasMoreTokens()) {
        String s = nextLine();
        if (s == null) {
          return false;
        }
        in = new StringTokenizer(s);
      }
      return true;
    }

    public String nextString() {
      return hasMoreTokens() ? in.nextToken() : null;
    }

    public String nextLine() {
      try {
        in = null;
        return br.readLine();
      } catch (Exception e) {
        e.printStackTrace();
        return null;
      }
    }

    public int nextInt() {
      return Integer.parseInt(nextString());
    }

    public long nextLong() {
      return Long.parseLong(nextString());
    }

  }

  static class OutputWriter extends PrintWriter {
    public OutputWriter(String fileName) throws FileNotFoundException {
      super(fileName);
    }

    public OutputWriter(OutputStream outputStream) {
      super(outputStream);
    }

    public OutputWriter(Writer writer) {
      super(writer);
    }

  }
}