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.io.File;
import java.io.FileNotFoundException;
import java.util.Scanner;
import java.util.Vector;


public class TaskB 
{

	/**
	 * @param args 
	 */
  int s, k;  
  
  public static void main(String[] args) throws FileNotFoundException
  {
    TaskB solver = new TaskB();
    solver.readInfo();
    solver.solve();
  }
  Vector<Integer> createKbonacciArray()
  {
    Vector<Integer> res = new Vector<Integer>();
    res.add(1);
    while (res.lastElement() < s)
    {
      int num = 0;
      for (int i = 1; i <= k; i++)
      {
        int ind = res.size() - i;
        if (ind < 0)
          break;
        num += res.get(ind);        
      }
      res.add(num);
    }
    //if (res.lastElement().intValue() == s)
//      res.remove(res.size() - 1);
    return res;
  }
  void solve()
  {
    Vector <Integer> kbonacci = createKbonacciArray();
    Vector <Integer> result = new Vector<Integer>();
    while (s > 0)
    {
      int i;
      for (i = kbonacci.size() - 1; i >= 0; i--)
        if (kbonacci.get(i).intValue() <= s)
          break;
      result.add(kbonacci.get(i));
      s -= kbonacci.get(i).intValue();
    }
  
    if (result.size() == 1)
      result.add(0);
    System.out.print(result.size() + "\n");
    for (int i = 0; i < result.size(); i++)
      System.out.print(result.get(i).toString() + " ");    
  }
  void readInfo() throws FileNotFoundException
  {
	//Scanner sc = new Scanner(new File("D:/programming/java/codeforces_139_b_kbonacci/bin/input2.txt"));
    Scanner sc = new Scanner(System.in);
	try
	{
	  s = sc.nextInt();
	  k = sc.nextInt();
	}
	finally
	{
      sc.close();
	}
  }
}