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>
const double pi = acos(-1.0);
using namespace std;
long long int gcd(long long int a, long long int b) {
  return b == 0 ? a : gcd(b, a % b);
}
long long int lcm(long long int a, long long int b) {
  return a * b / gcd(a, b);
}
void solve() {
  long long int s, k;
  cin >> s >> k;
  vector<long long int> v;
  deque<long long int> q;
  v.push_back(1);
  q.push_back(1);
  long long int sum = 0;
  while (sum < s) {
    sum += q.back();
    q.push_back(sum);
    v.push_back(q.back());
    if (q.size() > k) {
      sum -= q.front();
      q.pop_front();
    }
  }
  bool f = binary_search(v.begin(), v.end(), s);
  if (f) {
    cout << 2 << endl;
    cout << 0 << " " << s << endl;
  } else {
    vector<long long int> ans;
    reverse(v.begin(), v.end());
    for (auto x : v) {
      if (x <= s) {
        ans.push_back(x);
        s -= x;
      }
    }
    cout << ans.size() << endl;
    for (auto x : ans) {
      cout << x << " ";
    }
    cout << endl;
  }
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  solve();
  return 0;
}