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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int s, k, sum = 1;
  cin >> s >> k;
  vector<int> numbers;
  vector<int> answer;
  numbers.push_back(0);
  numbers.push_back(1);
  for (int i = 2; numbers[i - 1] < s; i++) {
    numbers.push_back(sum);
    sum = sum + sum;
    if (i - k >= 0) sum = sum - numbers[i - k];
  }
  for (int i = numbers.size() - 1; s > 0 && i >= 0; i--) {
    if (numbers[i] <= s) {
      answer.push_back(numbers[i]);
      s = s - numbers[i];
    }
  }
  if (answer.size() < 2) answer.push_back(0);
  cout << answer.size() << "\n";
  cout << answer[0];
  for (int i = 1; i < answer.size(); i++) cout << " " << answer[i];
}