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.*;
import java.util.*;

public class KthDivisor {
public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
        }

static class Solver {

    private void solve(InputReader inp, PrintWriter out) {
        long n = inp.nextLong();
        int k = inp.nextInt();

        LinkedList<Long> bs = new LinkedList<>();
        LinkedList<Long> as = new LinkedList<>();
        double sqrt = Math.sqrt(n);
        for (long i = 1; i < sqrt; i++) {
            if (n % i == 0) {
                bs.addLast(i);
                as.addFirst(n / i);
            }
        }
        if (sqrt % 1 == 0) bs.addLast((long) sqrt);
        if (k <= bs.size() + as.size()) {
            if (k <= bs.size()) out.print(bs.get(k - 1));
            else out.print(as.get(k - bs.size() - 1));
        } else out.print("-1");
    }
}

static class InputReader {
    BufferedReader reader;
    StringTokenizer tokenizer;

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

    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());
    }
}
}