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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.StringTokenizer;

public class A {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastScanner in = new FastScanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Solver solver = new Solver();
		solver.solve(in, out);
		out.close();
	}
}

class Solver {

	final int MAX_ROOT = 1000000;
	final int MAX_ANS = 100000;

	long k;

	boolean[] isPrime = new boolean[MAX_ROOT + 1];
	Map<Long, Boolean> divs = new HashMap<Long, Boolean>();
	List<Long> dArray = new ArrayList<Long>();
	List<Long> ans = new ArrayList<Long>();

	public void solve(FastScanner in, PrintWriter out) {

		long x = in.nextLong();
		k = in.nextLong();

		Arrays.fill(isPrime, true);
		isPrime[1] = false;

		divs.put(1L, false);
		for (long i = 1; i * i <= x; i++) {
			if (x % i == 0) {
				if (i == x / i) {
					divs.put(i, false);
					dArray.add(i);
				} else {
					divs.put(i, false);
					divs.put(x / i, false);
					dArray.add(i);
					dArray.add(x / i);
				}

			}
		}

		Collections.sort(dArray);

		for (long i = 1; i * i <= x; i++) {
			if (isPrime[(int) i]) {
				for (long j = i + i; j <= MAX_ROOT; j += i) {
					isPrime[(int) j] = false;
				}
			}
		}

		long t = x;
		for (int i = 2; i <= MAX_ROOT; i++) {
			if (isPrime[i]) {
				while (t % i == 0) {
					divs.put(Long.valueOf(i), true);
					t /= i;
				}
			}
		}
		divs.put(t, true);

		dfs(x, 0);

		for (int i = 0; i < MAX_ANS && i < ans.size(); i++) {
			out.print(ans.get(i));
			if (i + 1 == MAX_ANS || i + 1 == ans.size()) {
				out.println();
			} else {
				out.print(" ");
			}
		}
	}

	void dfs(long a, int depth) {
		if (ans.size() >= MAX_ANS) {
			return;
		}
		if (a == 1) {
			ans.add(a);
		} else if (divs.get(a)) {
			for (int i = 0; i < k - depth; i++) {
				if (ans.size() == MAX_ANS) {
					break;
				}
				ans.add(1L);
			}
			ans.add(a);
		} else if (depth == k) {
			ans.add(a);
		} else {
			for (int i = 0; i < dArray.size() && dArray.get(i) <= a; i++) {
				if (a % dArray.get(i) == 0) {
					dfs(dArray.get(i), depth + 1);
				}
			}
		}
	}

}

class FastScanner {

	private final BufferedReader in;
	private StringTokenizer st;

	public FastScanner(InputStream stream) {
		in = new BufferedReader(new InputStreamReader(stream));
	}

	public String next() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(in.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

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

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

	public double nextDouble() {
		return Double.parseDouble(next());
	}

}