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.math.BigInteger;
import java.util.*;
import java.io.*;

public class Main {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        FastReader() { br = new BufferedReader(new InputStreamReader(System.in)); }
        String next() { while (st == null || !st.hasMoreElements()) {
            try { st = new StringTokenizer(br.readLine()); }
            catch (IOException e) { e.printStackTrace(); } }
            return st.nextToken();
        }

        int nextInt() { return Integer.parseInt(next()); }
        long nextLong() { return Long.parseLong(next()); }
        double nextDouble() { return Double.parseDouble(next()); }

        String nextLine() {
            String str = "";
            try { str = br.readLine(); }
            catch (IOException e) { e.printStackTrace(); }
            return str;
        }
    }


    public static void main(String[] args) throws IOException {
        FastReader ip = new FastReader();
        OutputStream output = System.out;
        PrintWriter out = new PrintWriter(output);
        long n=ip.nextLong();
        long k=ip.nextLong();
        long c=0;
        int f=0;
        Stack<Long> stack=new Stack<>();
        for(long i=1;i<=Math.sqrt(n);i++){
            if(n%i==0){
                if((n/i)!=i) {
                    stack.add(n / i);
                }
                c++;
            }
            if(c==k){
                out.println(i);
                f=1;
                break;
            }
        }
        while(!stack.isEmpty()){
            long v=stack.pop();
            c++;
            if(c==k){
                out.println(v);
                f=1;
                break;
            }
        }
        if(f==0){
            out.println(-1);
        }
        out.close();
    }
}