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> V;
  V.push_back(1);
  int index = 0;
  long long sum = 0;
  while (sum <= (1LL << 35)) {
    sum += V[index++];
    if (index - k - 1 >= 0) sum -= V[index - k - 1];
    V.push_back(sum);
  }
  index = V.size() - 1;
  vector<int> javab;
  while (s) {
    if (s >= V[index]) {
      if (javab.size() || s != V[index]) {
        s -= V[index];
        javab.push_back(V[index]);
      } else {
        javab.push_back(V[index]);
        javab.push_back(0);
        break;
      }
    }
    index--;
  }
  cout << javab.size() << "\n";
  for (int i = 0; i < javab.size(); i++) cout << javab[i] << " ";
  return 0;
}