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() {
  long long s, k;
  cin >> s >> k;
  vector<long long> F;
  F.push_back(0);
  F.push_back(1);
  while (F.back() < 1.1e9) {
    int l = F.size();
    F.push_back(0);
    for (int i = max(0, l - (int)k); i <= l - 1; i++) {
      F[l] += F[i];
    }
  }
  vector<int> ans;
  long long last = -1;
  for (int i = (int)F.size() - 1; i >= 0; i--) {
    if (s >= F[i] && last != F[i]) {
      s -= F[i];
      ans.push_back(F[i]);
      last = F[i];
    }
  }
  sort(ans.begin(), ans.end());
  cout << ans.size() << endl;
  for (auto x : ans) {
    cout << x << " ";
  }
  cout << endl;
  return 0;
}