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.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;

public class Main {
    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter out;
    
    public static String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
    
    public static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    
    public static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    
    static final int maxn = 100000;
    static long b[];
    static ArrayList<Long> d;
    static ArrayList<Integer>[] e;
    static int bn, dn;
    
    static boolean add(long x) {
        if (bn < maxn) {
            b[bn++] = x;
        }
        return (bn < maxn);
    }
    
    static boolean print(int i, long k) {   
        //out.println(d.get(i) + " " + k);
        if (i == 0 || k == 0) {
            return add(d.get(i));
        }

        int sz = e[i].size();
        if (sz == 1) {
            for (int j = 0; j < k; ++j) {
                if (!add(1L)) {
                    return false;
                }
            }
            return add(d.get(i));
        }
    
        for (int j = 0; j < sz; ++j) {
            if (!print(e[i].get(j), k - 1)) {
                return false;
            }
        }
        return print(i, k - 1); 
    }
    
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        long x = nextLong();
        long k = nextLong();
        b = new long[111111];
        bn = 0;
        
        d = new ArrayList<>();  
        for (long y = 1; y * y <= x; ++y) if (x % y == 0) {
            d.add(y);
            if (y * y != x) d.add(x / y);
        }       
        Collections.sort(d);
        e = new ArrayList[d.size()];
        
        for (int i = 0; i < d.size(); ++i) {
            e[i] = new ArrayList<>();
            //out.println(d.get(i));
            //out.print("----> ");
            for (int j = 0; j < i; ++j) if (d.get(i) % d.get(j) == 0) {
                //out.print(d.get(j) + " ");
                e[i].add(j);
            }
            //out.println();
        }
        print(d.size() - 1, k);
        

        for (int i = 0; i < bn; ++i) {
            if (i > 0) out.print(" ");
            out.print(b[i]);
        }
        out.println();
        out.close();
    }

}