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.*;
import java.io.*;

public class Main implements Runnable {
        StringBuilder ans;
        int count = 0;
        int LIMIT = 100000;
        
	public void solve() throws IOException {
		long x = nextLong();
                long k = nextLong();
                ans = new StringBuilder();
                
                process(x, k);
                
                System.out.println(ans.toString());
	}
        
        void process(long x, long k){
            if(k == 0 || x == 1){
                ans.append(x + " ");
                count++;
            }
            else{
                ArrayList<Long> al = doit(x);
                for(int i = 0; i < al.size(); i++){
                    process(al.get(i), k-1);
                    if(count == LIMIT) return;
                }
            }
        }

        
        HashMap<Long, ArrayList<Long>> hmap = new HashMap<>();
        
        private ArrayList<Long> doit(long x){
            if(hmap.containsKey(x)) return hmap.get(x);
            
            ArrayList<Long> curLeft = new ArrayList<>();
            ArrayList<Long> curRight = new ArrayList<>();
            for(int i = 1; i * 1L * i <= x; i++){
                if(x % i == 0){
                    curLeft.add(i + 0L);
                    if(i * 1L * i != x)
                        curRight.add(x/i);
                }
            }
            
            for(int j = curRight.size() -1; j >= 0; j--) curLeft.add(curRight.get(j));
        
            ///TLE: changed the typecasting, and to LONG
            hmap.put(x, curLeft);
            
            return curLeft;
        }
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	//-----------------------------------------------------------
	public static void main(String[] args) {
		new Main().run();
	}

        public void print1Int(int[] a){
                for(int i = 0; i < a.length; i++)
                        System.out.print(a[i] + " ");
                System.out.println();
        }
        
        public void print2Int(int[][] a){
                for(int i = 0; i < a.length; i++){
                        for(int j = 0; j < a[0].length; j++){
                                System.out.print(a[i][j] + " ");
                        }
                        System.out.println();
                }
        }
        
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			tok = null;
			solve();
			in.close();
		} catch (IOException e) {
			System.exit(0);
		}
	}

	public String nextToken() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	public long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}

	BufferedReader in;
	StringTokenizer tok;
}