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.math.BigDecimal;
import java.net.URL;
import java.util.*;

public class Template implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine(), " :");
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int size) throws IOException {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    public static void main(String[] args) {
        new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    HashMap<Long, TreeSet<Long>> cache = new HashMap<>();

    TreeSet<Long> factorize(long x) {
        if (cache.containsKey(x)) return cache.get(x);
        TreeSet<Long> result = new TreeSet<>();
        for (int i = 1; (long) i * i <= x; i++) {
            if (x % i == 0) {
                result.add((long) i);
                result.add(x / i);
            }
        }
        cache.put(x, result);
        return result;
    }

    class Entry {
        long val;
        long cnt;

        public Entry(long val, long cnt) {
            this.val = val;
            this.cnt = cnt;
        }
    }

    void solve() throws IOException {
        long x = readLong();
        long k = readLong();

        if (x == 1) {
            out.println(1);
            return;
        }

        List<Entry> entries = new ArrayList<>();
        entries.add(new Entry(x, 1l));

        long index = 0;
        while (index < k) {
            index++;
            List<Entry> nextEntries = new ArrayList<>();
            long curLen = 0;
            for (Entry entry : entries) {
                if (entry.val == 1) {
                    nextEntries.add(new Entry(entry.val, entry.cnt));
                    curLen += entry.cnt;
                } else {
                    TreeSet<Long> set = factorize(entry.val);
                    for (Long val : set) {
                        if (val == 1) {
                            Entry last = nextEntries.size() == 0 ? null : nextEntries.get(nextEntries.size() - 1);
                            if (last != null && last.val == 1) {
                                last.cnt++;
                            } else {
                                nextEntries.add(new Entry(1, 1));
                            }
                        } else {
                            nextEntries.add(new Entry(val, 1));
                        }
                    }
                    curLen += set.size();
                }
                if (curLen > 100000) break;
            }
            entries = nextEntries;
            if (curLen > 100000 && nextEntries.size() == 1) break;

        }

        int printed = 0;
        for (Entry entry : entries) {
            for (int i = 0; i < entry.cnt; i++) {
                out.print(entry.val + " ");
                printed++;
                if (printed == 100000) break;
            }
            if (printed == 100000) break;
        }

    }


}