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.*;
import java.util.*;

public class TaskB
{
	private static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
	private static PrintWriter    writer = new PrintWriter   (System.out);

	private static StringTokenizer tokenizer;

	public static void main(String[] args)
	{
		long s = nextInt();
		long k = nextInt();

		List<Long> fibs = new ArrayList<Long>();
		fibs.add(new Long(1));

		long next = 0;
		while (next < s)
		{
			next = getLastElementsSum(fibs, k);
			fibs.add(new Long(next));
		}

		List<Long> ans = new LinkedList<Long>();
		int curInd = fibs.size() - 1;
		while (s > 0 && curInd >= 0)
		{
			if (s - fibs.get(curInd) >= 0)
			{
				ans.add(fibs.get(curInd));
				//writer.print(fibs.get(curInd) + " ");
				s -= fibs.get(curInd);
			}
			curInd--;
		}

		if (ans.size() < 2)
			ans.add(new Long(0));

		writer.println(ans.size());
		for (Long e : ans)
		{
			writer.print(e + " ");
		}
		
		writer.close();
	}

	private static long getLastElementsSum(List<Long> l, long n)
	{
		long sum = 0;

		int lastInd = l.size() - 1;
		int curInd  = lastInd;
		while (curInd >= 0 && lastInd - curInd < n)
		{
			sum += l.get(curInd);
			curInd--;
		}

		return sum;
	}

	private static String nextToken()
	{
		while (tokenizer == null || !tokenizer.hasMoreTokens())
		{
 			try
 			{
            	tokenizer = new StringTokenizer(reader.readLine());
            }
            catch (IOException e)
            {
                throw new RuntimeException(e);
            }
        }

        return tokenizer.nextToken();
	}

	private static int nextInt()
	{
        return Integer.parseInt(nextToken());
    }
}