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 p[10];
int main() {
  long long n, m;
  cin >> n >> m;
  vector<long long> vec;
  vec.push_back(0);
  vec.push_back(1);
  for (int i = 2;; i++) {
    long long sum = 0;
    for (int j = i - 1, k = 0; j >= 0 && k < m; j--, k++) sum += vec[j];
    vec.push_back(sum);
    if (sum > n) break;
  }
  vector<long long> ans;
  for (int i = vec.size() - 1; i >= 0; i--) {
    if (n >= vec[i]) {
      n -= vec[i];
      ans.push_back(vec[i]);
    }
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) cout << ans[i] << " ";
}