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.*;
public class P_255B {
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		
		int S = in.nextInt();
		int K = in.nextInt();
		
		ArrayList<Integer> ans = new ArrayList<Integer>();

		while (S > 0)
		{
			int tempans = kbin(S, K);
			S -= tempans;
			ans.add(tempans);
		}
		
		ans.add(0);
		
		System.out.println(ans.size());
		for (Integer i : ans)
			System.out.print(i + " ");
		System.out.println();
	}
	
	static int kbin(int S, int K)
	{
		int[] vals = new int[300];
		vals[0] = 1;
		
		int i = 1;
		int val = 0;
		for (; i < 300; ++i)
		{
			val += vals[i-1];
			if (i-K-1 >= 0) val -= vals[i-K-1];
			
			// System.out.println("kbin " + val + " " + i);
			vals[i] = val;
			
			if (val > S) break;
		}
		
		return vals[i-1];
	}
}