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.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Map;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Divisors {

	static final int MAX = (int) 1e5;

	static Map<Long, ArrayList<Long>> map;
	static ArrayList<Long> sol;

	static void solve(long x, long k) {
		if (sol.size() >= MAX)
			return;
		if (x == 1 || k == 0)
			sol.add(x);
		else {
			for (long d : map.get(x))
				solve(d, k - 1);
		}
	}

	static void sol() throws IOException {
		MyScanner sc = new MyScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		long x = sc.nextLong(), k = sc.nextLong();
		if (x == 1) {
			out.println(1);
		} else {
			ArrayList<Long> div = new ArrayList<>();
			for (long d = 1; d * d <= x; d++)
				if (x % d == 0) {
					div.add(d);
					if (x / d != d)
						div.add(x / d);
				}
			int n = div.size();
			Collections.sort(div);
			map = new TreeMap<>();
			for (int i = 0; i < n; i++) {
				long num = div.get(i);
				for (int j = 0; j <= i; j++)
					if (num % div.get(j) == 0) {
						ArrayList<Long> d = map.get(num);
						d = d == null ? new ArrayList<>() : d;
						d.add(div.get(j));
						map.put(num, d);
					}
			}
			sol = new ArrayList<>();
			solve(x, k);
			for (int i = 0; i < sol.size(); i++) {
				if (i > 0)
					out.print(" ");
				out.print(sol.get(i));
			}
		}
		out.flush();
		out.close();
	}

	public static void main(String[] args) throws IOException {
		new Thread(null, new Runnable() {

			@Override
			public void run() {
				try {
					sol();
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
		}, "1", 1 << 27).start();
	}

	static class MyScanner {

		BufferedReader br;
		StringTokenizer st;

		MyScanner(InputStream is) {
			br = new BufferedReader(new InputStreamReader(is));
		}

		MyScanner(String filename) throws IOException {
			br = new BufferedReader(new FileReader(new File(filename)));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		boolean ready() throws IOException {
			return br.ready();
		}
	}
}