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.PrintWriter;
import java.util.*;

/**
 * Created by hama_du on 2014/07/19.
 */
public class ProblemE {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        long X = in.nextLong();
        long k = in.nextLong();


        long[] answer = solve(X, k);
        StringBuilder b = new StringBuilder();
        for (int i = 0 ; i < answer.length ; i++) {
            b.append(' ').append(answer[i]);
        }
        out.println(b.substring(1));
        out.flush();
    }

    private static long[] solve(long x, long k) {
        if (x == 1) {
            return new long[]{1};
        }
        if (k > 100000) {
            long[] ret = new long[100000];
            Arrays.fill(ret, 1);
            return ret;
        }

        List<Long> divisors = new ArrayList<Long>();
        for (long d = 1 ; d * d <= x ; d++) {
            if (x % d == 0) {
                divisors.add(d);
                if (d * d != x) {
                    divisors.add(x / d);
                }
            }
        }
        Collections.sort(divisors);

        // debug(divisors);

        Map<Long,List<Long>> dmap = new HashMap<Long,List<Long>>();
        for (long d : divisors) {
            List<Long> div = new ArrayList<Long>();
            for (long e : divisors) {
                if (d % e == 0) {
                    div.add(e);
                }
                if (d < e) {
                    break;
                }
            }
            dmap.put(d, div);
        }


        List<Long> numbers = new ArrayList<Long>();
        numbers.add(x);

        int offset = 0;
        for (int _k = 0 ; _k < k ; _k++) {
            List<Long> nextNumbers = new ArrayList<Long>();
            int ln = numbers.size()-1;

            nextNumbers.clear();

            long one = 0;
            long size = 0;
            buildNext: for (int d = 0 ; d < numbers.size() ; d++) {
                Long dec = numbers.get(d);
                if (dec <= -1) {
                    one -= dec;
                    continue;
                }
                for (long ne : dmap.get(dec)) {
                    if (ne == 1) {
                        one++;
                        continue;
                    } else {
                        if (one >= 1) {
                            nextNumbers.add(-one);
                            size += (one-1);
                            one = 0;
                        }
                    }
                    nextNumbers.add(ne);
                    if (nextNumbers.size() + size >= 110000) {
                        break buildNext;
                    }
                }
            }
            numbers = nextNumbers;
        }

        long[] answer = new long[100000];
        Arrays.fill(answer, -1);
        int idx = 0;
        for (long nu : numbers) {
            if (nu < 0) {
                for (long l = 0 ; l < (-nu) ; l++) {
                    answer[idx++] = 1;
                    if (idx >= 100000) {
                        break;
                    }
                }
            }  else {
                answer[idx++] = nu;
            }
            if (idx >= 100000) {
                break;
            }
        }



        long[] ret = new long[idx];
        for (int i = 0 ; i < idx ; i++) {
            ret[i] = answer[i];
        }
        return ret;
    }

    private static List<Long> generatePrimes(int max) {
        boolean[] filtered = new boolean[max+1];
        filtered[0] = filtered[1] = true;
        for (int i = 2 ; i <= max ; i++) {
            if (!filtered[i]) {
                for (int ii = i * 2 ; ii <= max ; ii += i) {
                    filtered[ii] = true;
                }
            }
        }

        List<Long> primes = new ArrayList<>();
        for (int i = 0 ; i <= max ; i++) {
            if (!filtered[i]) {
                primes.add(i + 0L);
            }
        }
        return primes;
    }

    private static long doit(long med, long r, long c) {
        long cnt = 0;
        for (long i = 1 ; i <= r ; i++) {
            cnt += Math.min(med / i, c);
        }
        return cnt;
    }

    private static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}