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 f[1005];
vector<int> v;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int s, k, i = 1;
  cin >> s >> k;
  f[0] = 1;
  f[1] = 1;
  while (f[i] <= s) {
    i++;
    f[i] = 2 * f[i - 1] - ((i > k) ? f[i - k - 1] : 0);
  }
  for (int j = i - 1; j >= 0; j--) {
    if ((s - f[j]) >= 0) {
      v.push_back(f[j]);
      s -= f[j];
    }
    if (s == 0) break;
  }
  v.push_back(0);
  cout << v.size() << endl;
  for (int i = 0; i < v.size(); i++) {
    cout << v[i] << " ";
  }
}