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.*;
import java.util.function.IntBinaryOperator;

public class Solver {
    private BufferedReader in;
    private PrintWriter out;

    Solver () {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter(new FileWriter("output.txt"));
        } catch (Exception ex) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
        try {
            solve();
        } catch (Exception ex) {
            ex.printStackTrace();
        } finally {
            try {
                in.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
            out.close();
        }
    }

    public static void main(String[] args) {
        new Solver();
    }

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

    String nextLine() throws IOException {
        return in.readLine();
    }

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

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

    void solve() throws IOException {
        long n = nextLong();
        int k = nextInt();
        Set<Long> dels = new TreeSet<>();
        final int SIZE = 32000000;
        for (long i = 1; i < SIZE; i++) {
            if (n % i == 0) {
                dels.add(i);
                dels.add(n/i);
            }
        }
        dels.add(n);
        System.err.println(dels);
        if (dels.size() < k)
            out.print(-1);
        else {
            List<Long> lDels = new ArrayList<>(dels);
            out.print(lDels.get(k - 1));
        }
    }

}