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:
//package practice.E;

import java.io.*;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.StringTokenizer;

public class CF448E {
    static HashMap<Long, Integer> map;
    static ArrayList<Long>[] divs;
    static PrintWriter pw;
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);

        long x = sc.nextLong();
        k = sc.nextLong();
        if(x == 1){
            System.out.println(1);
            return;
        }

        if(k >= 100000){
            for (int i = 0; i < 100000; i++) {
                if(i != 0)
                    pw.print(" ");
                pw.print(1);
            }
            pw.println();
            pw.flush();
            pw.close();
            return;
        }


        ArrayList<Long> div = new ArrayList<>();
        for (long i = 1; i*i <= x; i++) {
            if(x%i == 0){
                div.add(i);
                if(i != x/i)
                    div.add(x/i);
            }
        }

        Collections.sort(div);
        map = new HashMap<>();
        for (int i = 0; i < div.size(); i++) {
            map.put(div.get(i), i);
        }


        divs = new ArrayList[div.size()];
        for (int i = 0; i < div.size(); i++) {
            divs[i] = new ArrayList<>();
            for (int j = 0; j <= i; j++) {
                if(div.get(i)%div.get(j) == 0)
                    divs[i].add(div.get(j));
            }
        }

        dfs(x, (int)k);

        pw.flush();
        pw.close();
    }

    static int printed = 0;
    static long k;
    static void dfs(long x, int rem){
        if(printed == 100000)
            return;

        if(rem == 0) {
            pw.print(x + " ");
            printed++;
            return;
        }

        if(x == 1) {
            pw.print(x + " ");
            printed++;
            return;
        }

        for (long div :divs[map.get(x)]) {
            dfs(div, rem-1);
        }
    }

    static class Scanner
    {
        StringTokenizer st; BufferedReader br;
        public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
        public Scanner(String s) throws FileNotFoundException {	br = new BufferedReader(new FileReader(new File(s)));}
        public String next() throws IOException {while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());return st.nextToken();}
        public int nextInt() throws IOException {return Integer.parseInt(next());}
        public long nextLong() throws IOException {return Long.parseLong(next());}
        public String nextLine() throws IOException {return br.readLine();}
        public boolean ready() throws IOException {return br.ready();}
    }
}