Problem: Bizon the Champion isn't just friendly, he also is a rigorous coder.

Let's define function f(a), where a is a sequence of integers. Function f(a) returns the following sequence: first all divisors of a1 go in the increasing order, then all divisors of a2 go in the increasing order, and so on till the last element of sequence a. For example, f([2, 9, 1]) = [1, 2, 1, 3, 9, 1].

Let's determine the sequence Xi, for integer i (i ≥ 0): X0 = [X] ([X] is a sequence consisting of a single number X), Xi = f(Xi - 1) (i > 0). For example, at X = 6 we get X0 = [6], X1 = [1, 2, 3, 6], X2 = [1, 1, 2, 1, 3, 1, 2, 3, 6].

Given the numbers X and k, find the sequence Xk. As the answer can be rather large, find only the first 105 elements of this sequence.

Input

A single line contains two space-separated integers — X (1 ≤ X ≤ 1012) and k (0 ≤ k ≤ 1018).

Output

Print the elements of the sequence Xk in a single line, separated by a space. If the number of elements exceeds 105, then print only the first 105 elements.

Examples

Input

6 1


Output

1 2 3 6 


Input

4 2


Output

1 1 2 1 2 4 


Input

10 3


Output

1 1 1 2 1 1 5 1 1 2 1 5 1 2 5 10 

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileReader;
import java.util.Vector;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Agostinho Junior (junior94)
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskE solver = new TaskE();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskE {
	OutputWriter out;
	InputReader in;
	Vector<Long> divisors = new Vector<Long>();
	int count;
	public void solve(int testNumber, InputReader in, OutputWriter out) {
		this.in = in; this.out = out;
		long x = in.readLong();
		long k = in.readLong();
		generate(x);
		count = (int)1e5;
		rec(x, k);
	}
	public void rec(long x, long k) {
		if (k == 0 || x == 1) {
			out.print(x + " ");
			count--;
		} else for(long number: divisors) {
			if (number > x || count == 0) {
				break;
			}
			if (x % number == 0) {
				rec(number, k - 1);
			}
		}
	}
	public void generate(long x) {
		long max = (long)Math.sqrt(x);
		Vector<Long> larger = new Vector<Long>();
		for (long i = 1; i <= max; i++) if (x % i == 0) {
			divisors.add(i);
			if (x / i != i) {
				larger.add(x / i);
			}
		}
		for (int i = larger.size() - 1; i >= 0; i--) {
			divisors.add(larger.get(i));
		}
	}
}

class OutputWriter {
	private PrintWriter output;
	public OutputWriter() {
		this(System.out);
	}
	public OutputWriter(OutputStream out) {
		output = new PrintWriter(out);
	}
	public OutputWriter(Writer writer) {
		output = new PrintWriter(writer);
	}
	public void print(Object o) {
		output.print(o);
	}

	public void close() {
		output.close();
	}
}

class InputReader {
	private BufferedReader input;
	private StringTokenizer line = new StringTokenizer("");
	public InputReader() {
		this(System.in);
	}
	public InputReader(InputStream in) {
		input = new BufferedReader(new InputStreamReader(in));
	}
	public InputReader(String s) {
		try {
			input = new BufferedReader(new FileReader(s));
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	public void fill() {
		try {
			if(!line.hasMoreTokens()) line = new StringTokenizer(input.readLine());
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}

	public long readLong() {
		fill();
		return Long.parseLong(line.nextToken());
	}
}