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.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        InputStream is = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(is);
        PrintWriter out = new PrintWriter(outputStream);
        new Task().solve(in, out);
        out.close();
    }
}

class Task {

    public static List<Long> tt = new ArrayList<Long>();

    public static Map<Long, List<Long>> facs = new HashMap<Long, List<Long>>();

    public static final int N = (int) 1e5;

    public static int rem = (int) 1e5;

    public void solve(InputReader in, PrintWriter out) {
        long x = in.nextLong();
        long k = in.nextLong();

        for (long i = 1; i * i <= x; ++i) {
            if (x % i == 0) {
                tt.add(i);
                if (i * i != x) {
                    tt.add(x / i);
                }
            }
        }

        Collections.sort(tt);

        for (Long L : tt) {
            List<Long> curFac = new ArrayList<Long>();
            for (Long ano : tt) {
                if (ano > L) {
                    break;
                }
                if (L % ano == 0) {
                    curFac.add(ano);
                }
            }
            facs.put(L, curFac);
        }
        List<Long> arr = new ArrayList<Long>();
        gao(arr, x, k);
        for (Long a : arr) {
            out.print(a + " ");
        }
        out.println();
    }

    public static void gao(List<Long> ret, long n, long remTime) {
        if (ret.size() == N) {
            return;
        }
        if (remTime == 0 || n == 1) {
            ret.add(n);
            return;
        }
        List<Long> cur = facs.get(n);
        for (Long t : cur) {
            gao(ret, t, remTime - 1);
        }
    }
}

class InputReader {
    public BufferedReader reader;

    public StringTokenizer tokenizer;

    public InputReader(InputStream is) {
        reader = new BufferedReader(new InputStreamReader(is));
        tokenizer = null;
    }

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

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

}