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.*;
import java.util.*;
import java.math.*;


public class Solution {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer tok;
	
	
	static void solve() throws Exception {
		long x = nextLong();
		long k = nextLong();
		dfs(x, k);
		out.println();
	}
	
	static int cnt = 0;
	
	static void dfs(long x, long k) {
		if (k == 0 || x == 1) {
			out.print(x + " ");
			++cnt;
		} else {
			ArrayList<Long> a = getD(x);
			for (int i = 0; i < a.size(); ++i) {
				dfs(a.get(i), k - 1);
				if (cnt == (int) (1e5)) {
					return;
				}
			}
		}
	}
	
	static HashMap<Long, ArrayList<Long>> d = new HashMap<Long, ArrayList<Long>>();
	
	static ArrayList<Long> getD(long x) {
		if (d.containsKey(x)) {
			return d.get(x);
		}
		ArrayList<Long> res1 = new ArrayList<Long>();
		ArrayList<Long> res2 = new ArrayList<Long>();
		for (long i = 1; i*i <= x; ++i) {
			if (x % i == 0) {
				res1.add(i);
				if (i*i != x) {
					res2.add(x / i);
				}
			}
		}
		Collections.reverse(res2);
		res1.addAll(res2);
		d.put(x, res1);
		return res1;
	}
	
	static int sqr(int x) {
		return x*x;
	}
	
	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());
	}

	static BigInteger nextBigInteger() throws IOException {
		return new BigInteger(next());
	}
	
	static String next() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}
	
	static String nextLine() throws IOException {
		tok = new StringTokenizer("");
		return in.readLine();
	}

	static boolean hasNext() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			String s = in.readLine();
			if (s == null) {
				return false;
			}
			tok = new StringTokenizer(s);
		}
		return true;
	}

	public static void main(String args[]) {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(new OutputStreamWriter(System.out));
			//in = new BufferedReader(new FileReader("input.in"));
			//out = new PrintWriter(new FileWriter("output.out"));
			solve();
			in.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			java.lang.System.exit(1);
		}
	}
}