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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXLEN = 1e5;
map<long long, vector<long long> > divisors;
vector<long long> f(long long X, long long k) {
  if (k == 0) {
    return vector<long long>({X});
  }
  if (k & 1) {
    vector<long long> ret;
    for (long long d : divisors[X]) {
      vector<long long> tmp = f(d, k - 1);
      for (int i = 0; i < tmp.size() and ret.size() < MAXLEN; i++) {
        ret.push_back(tmp[i]);
      }
      if (ret.size() == MAXLEN) break;
    }
    return ret;
  }
  vector<long long> tmp = f(X, k >> 1);
  map<long long, int> first_pos;
  for (int i = 0; i < tmp.size(); i++) {
    if (!first_pos.count(tmp[i])) {
      first_pos[tmp[i]] = i;
    }
  }
  map<long long, pair<int, int> > range;
  range[1] = pair<int, int>(0, 0);
  long long d0 = 1;
  for (long long d1 : divisors[X]) {
    if (d1 == 1) continue;
    range[d1] = pair<int, int>(first_pos[d0] + 1, first_pos[d1]);
    d0 = d1;
  }
  vector<long long> tmp2;
  for (int i = 0; i < tmp.size() and tmp2.size() < MAXLEN; i++) {
    int j0 = range[tmp[i]].first, j1 = range[tmp[i]].second;
    for (int j = j0; j <= j1; j++) tmp2.push_back(tmp[j]);
  }
  tmp = tmp2;
  vector<long long> ret;
  for (int i = 0; i < tmp.size() and ret.size() < MAXLEN; i++) {
    for (long long d : divisors[tmp[i]]) {
      ret.push_back(d);
      if (ret.size() == MAXLEN) break;
    }
  }
  return ret;
}
int main() {
  long long X, k;
  while (scanf("%lld%lld", &X, &k) > 0) {
    if (X == 1) {
      printf("1\n");
      continue;
    }
    if (k >= MAXLEN) {
      for (int i = 0; i < MAXLEN; i++) {
        if (i) printf(" ");
        printf("1");
      }
      printf("\n");
      continue;
    }
    divisors.clear();
    for (long long d = 1; d * d <= X; d++) {
      if (X % d == 0) {
        divisors[X].push_back(d);
        if (d * d != X) divisors[X].push_back(X / d);
      }
    }
    sort(divisors[X].begin(), divisors[X].end());
    for (long long Y : divisors[X]) {
      if (X == Y) break;
      for (long long d : divisors[X]) {
        if (Y % d == 0) divisors[Y].push_back(d);
        if (d == Y) break;
      }
    }
    vector<long long> Xk = f(X, k);
    for (int i = 0; i < Xk.size(); i++) {
      if (i) printf(" ");
      printf("%lld", Xk[i]);
    }
    printf("\n");
  }
}