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

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

class TaskE {
	public void solve(int testNumber, FastScanner in, PrintWriter out) {
		this.out = out;
		long x = in.nextLong();
		long k = in.nextLong();
		divisors = getDivisors(x);
		children = new int[divisors.length][];
		for (int i = 0; i < divisors.length; i++) {
			long[] d = getDivisors(divisors[i]);
			children[i] = new int[d.length];
			for (int j = 0; j < d.length; j++) {
				children[i][j] = Arrays.binarySearch(divisors, d[j]);
			}
		}
		rec(divisors.length - 1, k);
	}

	final int N = 100000;
	int numPrinted;
	PrintWriter out;
	long[] divisors;
	int[][] children;

	private boolean rec(int i, long k) {
		if (k == 0) {
			return print(i);
		}
		if (!print(0)) {
			return false;
		}
		for (int j : children[i]) {
			if (j == 0) {
				continue;
			}
			if (!rec(j, k - 1)) {
				break;
			}
		}
		return true;
	}

	private boolean print(int id) {
		if (numPrinted == N) {
			return false;
		}
		if (numPrinted > 0) {
			out.print(" ");
		}
		out.print(divisors[id]);
		++numPrinted;
		return true;
	}

	private long[] getDivisors(long x) {
		List<Long> list = new ArrayList<Long>();
		for (long i = 1; i*i <= x; i++) {
			if (x % i == 0) {
				list.add(i);
				if (i*i < x) {
					list.add(x / i);
				}
			}
		}
		Collections.sort(list);
		long[] d = new long[list.size()];
		for (int i = 0; i < list.size(); i++) {
			d[i] = list.get(i);
		}
		return d;
	}

}

class FastScanner {

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

}