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 s, k;
long long fib[100];
int main() {
  scanf("%d %d", &s, &k);
  int i;
  fib[0] = 1;
  for (i = k + 1; fib[i - k - 1] <= s; ++i)
    for (int j = max(k, i - k); j < i; ++j) fib[i - k] += fib[j - k];
  vector<int> v;
  for (int j = i - 1; s > 0 and j >= k; --j)
    if (fib[j - k] <= s) {
      v.push_back(fib[j - k]);
      s -= fib[j - k];
    }
  if (v.size() == 1)
    printf("2\n%d 0", v[0]);
  else {
    printf("%d\n", v.size());
    for (int i = 0; i < v.size(); ++i) printf("%d ", v[i]);
  }
  puts("");
  return 0;
}