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.StringTokenizer;

/**
 * @author flame239
 */

public class KDivider {
    FastScanner in;
    PrintWriter out;

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
            st = null;
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

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


    public static void main(String[] args) {
        new KDivider().run();
    }

    public void run() {
        in = new FastScanner();
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    //////////////////////////////////
    public void solve() {
        long n = in.nextLong();
        int k = in.nextInt();

        ArrayList<Integer> smallDividers = new ArrayList<Integer>();

        int nSqrt = (int) Math.floor(Math.sqrt(n));
        for (int i = 1; i <= nSqrt; i++) {
            if (n % i == 0) {
                smallDividers.add(i);
            }
        }

        int smallDivCount = smallDividers.size();
        boolean hasSqrt = (long)smallDividers.get(smallDivCount - 1) * smallDividers.get(smallDivCount - 1) == n;

        int divCount = hasSqrt ? smallDivCount * 2 - 1 : smallDivCount * 2;
        if (k > divCount) {
            out.print("-1");
        } else if (k <= smallDivCount) {
            out.print(smallDividers.get(k - 1));
        } else {
            int pairDivider = smallDividers.get(divCount - k);
            out.print(n / pairDivider);
        }
    }
}