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.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Solution3 {
	public static void main(String[] args){
		 	FastReader sc = new FastReader();
	        long n = sc.nextLong();
	        long k = sc.nextLong();
	        long ans = divisor(n,(int)k);
	        System.out.println(ans);
	}
	public static long divisor(long n,int k){
		long count = 1;
		long count2 = 0;
		long length = 0;
		long answer = 0;
		for(int i = 1;i <= Math.sqrt(n);i++){
			if(n % i == 0){
				count2++;
			}
		}
		if(n % Math.sqrt(n) == 0){
			length = count2 * 2 - 1;
		}
		else{
			length = count2 * 2;
		}
		//System.out.println(length);
		if(k > length){
			return -1;
		}
		for(long i = 1;i <= Math.sqrt(n);i++){
			if(n % i == 0){
				if(k == count){
					answer = i;
					break;
				}
				if(i != Math.sqrt(n)){
					if(k == length - count + 1){
						answer =  n/i;
						break;
					}
				}
				count++;
			}
		}
		return answer;
	}
	static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public 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;
        }
    }
}