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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Stack;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.logging.Level;
import java.util.logging.Logger;

public class Main {

    
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        InputReader in = new InputReader(inputStream);
        
        ArrayList<Long> L=new ArrayList<Long>();
        long n = in.nextLong(); int k=in.nextInt();
        long max=41622776;
        for(long i=1;i<=max;i++){
            if(n%i==0 && i<n/i){
                L.add(i);
                L.add(n/i);
            }
        }
        long t = (long)Math.sqrt(n);
        if(t*t==n)L.add(t);
        Collections.sort(L);
        
        if(k<=L.size())out.println(L.get(k-1));
        else out.println(-1);
        out.close();
    }

    static class InputReader {

        BufferedReader reader;
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream), 32624);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException ex) {
                    Logger.getLogger(Main.class.getName()).log(Level.SEVERE, null, ex);
                }
            }
            return tokenizer.nextToken();
        }

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

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

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

        public int[] nextArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public double[] nextArrayd(int n) {
            double[] a = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextDouble();
            }
            return a;
        }

        private BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

        public void printAr(int[] a) {
            System.out.print("[");
            for (long x : a) {
                System.out.print(x + ",");
            }
            System.out.print("]");
        }
    }

}