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.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;


public class q5 {
	static ArrayList<Integer>[] gph;
	
	public static void main(String[] args) throws IOException {
		
		Reader.init(System.in);
		PrintWriter out=new PrintWriter(System.out);
		StringBuffer output=new StringBuffer(""),output2=new StringBuffer("");
		long n=Reader.nextLong();
		int k=Reader.nextInt()-1;
		ArrayList<Long> div=new ArrayList<Long>();
		long sq=(long) Math.sqrt(n);
		for(long i=1;i<=sq;i++) {
			if(n%i==0) {
				div.add(i);
				if(i!=n/i) div.add(n/i);
			}
		}
		Collections.sort(div);
		if(div.size()<=k) out.println(-1);
		else out.print(div.get(k));
		out.flush();
	}
}



class NoD{
	int a, b;
	NoD(int aa,int bb){
		a=Math.min(aa, bb);b=Math.max(aa, bb);
	}
}







class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    /** get next word */
    static String nextLine() throws IOException{
    	return reader.readLine();
    }
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }
    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}