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() {
  int i, s, k, j, sum;
  vector<int> v;
  vector<int> vivod;
  cin >> s >> k;
  if (s == 1) {
    cout << 2 << endl;
    cout << 0 << " " << 1;
    return 0;
  }
  if (k <= 100) {
    for (i = 0; i < k; i++) v.push_back(0);
    v.push_back(1);
    i = k;
    while (v[i] <= s) {
      sum = 0;
      for (j = 0; j < k; j++) sum += v[i - j];
      v.push_back(sum);
      i++;
    }
    v.pop_back();
  } else {
    v.push_back(1);
    sum = 1;
    i = 0;
    while (v[i] <= s) {
      v.push_back(sum);
      sum = sum * 2;
      i++;
    }
    v.pop_back();
  }
  if (s == v[v.size() - 1]) {
    cout << 2 << endl;
    cout << 0 << " " << s;
    return 0;
  }
  while (s > 0) {
    if (s >= v[v.size() - 1]) {
      s = s - v[v.size() - 1];
      vivod.push_back(v[v.size() - 1]);
    }
    v.pop_back();
  }
  cout << vivod.size() << endl;
  for (i = 0; i < vivod.size(); i++) cout << vivod[i] << " ";
  return 0;
}