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.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Round256_E {

    long MAX = 100000 + 5;
    long[] factors;

    long cnt;

    long K;

    StringBuffer ans;
    boolean first;

    int cc =0;
    public void print(long val) {
        if (first) {
            first = false;
        } else {
            ans.append(' ');
//          System.out.println(++cc);
        }
        ans.append(String.valueOf(val));
    }

    public void go(int from, int to, long level) {
//      System.out.println(from + " " + to + " " + level);
        if (level == K || to == 0) {
            ++cnt;
            print(factors[to]);
            return;
        }
        for (int j = from; cnt < 100000 && j <= to; j++) {
            if (factors[to] % factors[j] == 0) {
                go(from, j, level + 1);
            }
        }

    }

    public void solve() throws Exception {
        InputReader in = new InputReader();

        long X = in.nextLong();
        K = Math.min(MAX, in.nextLong());

        if(X == 1){
            System.out.println(1);
            return;
        }
        // build factors
        factors = new long[(int) MAX];
        int to = 0;
        for (long i = 2; to < factors.length && i <= (long)(.5+Math.sqrt(X)); i++) {
            if (X % i == 0) {
                factors[to++] = i;
                if(X/i != i){
                    factors[to++] = X/i;
                }
            }
        }
        factors[to++] = 1;
        factors[to] = X;
        Arrays.sort(factors, 0, to+1);
        cnt = 0;
        ans = new StringBuffer();
        first = true;
        go(0, to, 0);
        System.out.println(ans);
// 1000000000000 1000000000000000000
    }

    public static void main(String[] args) throws Exception {
        new Round256_E().solve();
    }

    static class InputReader {
        BufferedReader in;
        StringTokenizer st;

        public InputReader() throws IOException {
            in = new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer(in.readLine());

        }

        public String next() throws IOException {

            while (!st.hasMoreElements())
                st = new StringTokenizer(in.readLine());
            return st.nextToken();
        }

        public int nextInt() throws NumberFormatException, IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws NumberFormatException, IOException {
            return Long.parseLong(next());
        }
    }

}