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 JAVA):

Solution:
import java.util.ArrayList;
import java.util.Scanner;

public class WellKnownNumbers implements Runnable {
  public void run() {
    try {
      Scanner in = new Scanner(System.in);
      //BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
      long s = in.nextInt();
      long k = in.nextInt();
      ArrayList<Long> p = new ArrayList<Long>();
      p.add(1L);
      while (p.get(p.size() - 1) < s) {
        long n = 0;
        for (int i = 0; i < Math.min(k, p.size()); i++) {
          n += p.get(p.size() - 1 - i);
        }
        p.add(n);
      }
      ArrayList<Long> res = new ArrayList<Long>();
      res.add(0L);
      int i = p.size() - 1;
      while (p.get(i) > s) i--;
      res.add(p.get(i));
      s -= p.get(i);
      i--;
      while (s != 0) {
        while (p.get(i) > s) i--;
        res.add(p.get(i));
        s -= p.get(i);
      }
      System.out.println(res.size());
      for (int j = 0; j < res.size(); j++) {
        System.out.print(res.get(j) + " ");
      }
      System.out.println();
    } catch (Exception e) {
      throw new RuntimeException(e);
    }
  }

  public static void main(String[] args) {
    new Thread(new WellKnownNumbers()).start();
  }
}