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;
const int z = 1000;
int fibs[z];
int max(int a, int b) {
  if (a > b)
    return a;
  else
    return b;
}
int fib(int n, int k) {
  if (n < k)
    return 0;
  else {
    if (n == k)
      return 1;
    else {
      int sum = 0;
      for (int i = max(n - k, k); i < n; ++i)
        if (i >= k && i < k + z)
          sum += fibs[i - k];
        else
          sum += fib(i, k);
      return sum;
    }
  }
}
int main() {
  int s, k;
  cin >> s >> k;
  fibs[0] = 1;
  for (int i = 1; i < z; ++i) {
    fibs[i] = 0;
    for (int j = max(i - k, 0); j < i; ++j)
      if (j >= 0) fibs[i] += fibs[j];
  }
  bool first = true;
  int arr[100000];
  int sz = 1;
  arr[0] = 0;
  while (s > 0) {
    int j = 0, c = k - 1, p = 0;
    while (s > j) {
      c++;
      p = j;
      j = fib(c, k);
    }
    if (j > s) {
      s -= p;
      arr[sz] = p;
      sz++;
    } else {
      s -= j;
      arr[sz] = j;
      sz++;
    }
    first = false;
  }
  cout << sz << endl;
  for (int i = 0; i < sz; ++i) {
    cout << arr[i] << " ";
  }
  return 0;
}