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;
bool isprime(long long int n) {
  if (n < 2) return false;
  for (long long int i = 2; i <= sqrt(n); i++)
    if (n % i == 0) return false;
  return true;
}
long long gcd(long long int a, long long int b) {
  if (a == 0 || b == 0)
    return a + b;
  else
    return gcd(b, a % b);
}
void MAIN();
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  MAIN();
  return 0;
}
long long int num[1001], sum[1001];
void MAIN() {
  num[0] = 1;
  sum[0] = 1;
  long long int s, k;
  cin >> s >> k;
  long long int i = 0;
  while (s > num[i]) {
    num[i + 1] = sum[i] - ((i - k) >= 0 ? sum[i - k] : 0);
    sum[i + 1] = sum[i] + num[i + 1];
    i++;
  }
  vector<long long int> ans;
  for (i; i >= 0 && s >= 0; i--) {
    if (num[i] <= s) {
      ans.push_back(num[i]);
      s -= num[i];
    }
  }
  if ((long long int)(ans).size() == 1) ans.push_back(0);
  cout << (long long int)(ans).size() << endl;
  for (long long int i = 0; i < (long long int)(ans).size(); i++)
    cout << ans[i] << ' ';
}