Problem: Numbers k-bonacci (k is integer, k > 1) are a generalization of Fibonacci numbers and are determined as follows:

  * F(k, n) = 0, for integer n, 1 ≤ n < k; 
  * F(k, k) = 1; 
  * F(k, n) = F(k, n - 1) + F(k, n - 2) + ... + F(k, n - k), for integer n, n > k. 



Note that we determine the k-bonacci numbers, F(k, n), only for integer values of n and k.

You've got a number s, represent it as a sum of several (at least two) distinct k-bonacci numbers. 

Input

The first line contains two integers s and k (1 ≤ s, k ≤ 109; k > 1).

Output

In the first line print an integer m (m ≥ 2) that shows how many numbers are in the found representation. In the second line print m distinct integers a1, a2, ..., am. Each printed integer should be a k-bonacci number. The sum of printed integers must equal s.

It is guaranteed that the answer exists. If there are several possible answers, print any of them.

Examples

Input

5 2


Output

3
0 2 3


Input

21 5


Output

3
4 1 16

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int s, k;
  cin >> s >> k;
  if (s == 1) {
    cout << "2\n1 0";
    return 0;
  }
  vector<int> two_in;
  two_in.push_back(1);
  two_in.push_back(1);
  for (int i = 2;; i++) {
    two_in.push_back(two_in.back() * 2);
    if (two_in.back() >= s) {
      if (two_in.back() == s) {
        cout << "2\n0 " << s;
        return 0;
      }
      vector<int> ans;
      for (int j = i - 1; j >= 0; j--)
        if (two_in[j] <= s) {
          s -= two_in[j];
          ans.push_back(two_in[j]);
        }
      cout << ans.size() << endl;
      for (int j = 0; j < ans.size(); j++) cout << ans[j] << ' ';
      return 0;
    }
    if (i == k) break;
  }
  int l = 0;
  do {
    two_in.push_back(2 * two_in.back() - two_in[l]);
    l++;
  } while (two_in.back() < s);
  vector<int> ans;
  for (int j = two_in.size() - 2; j >= 0; j--)
    if (s >= two_in[j]) {
      s -= two_in[j];
      ans.push_back(two_in[j]);
    }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) cout << ans[i] << ' ';
  return 0;
}