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 {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int s = sc.nextInt();
		int k = sc.nextInt();

		ArrayList<Long> bon = new ArrayList<Long>();
		ArrayList<Long> cum = new ArrayList<Long>();

		bon.add(1l);
		
		cum.add(1l);
		
		while(bon.get(bon.size()-1)<s)
		{
			bon.add(cum.get(cum.size()-1 )-  (cum.size()-1-k>=0?cum.get(cum.size()-1-k):0));
			cum.add(bon.get(bon.size()-1) + cum.get(cum.size()-1));
		}
		
		bon.add(0, 0l);
		
		//System.out.println(bon.get());
		int idx = bon.size()-1;
		int c = 0;
		StringBuilder sb = new StringBuilder();
		while(idx>0 && s>0)
		{
			if(bon.get(idx)>s)
				idx--;
			else
			{
				sb.append(bon.get(idx) + " ");
				s-=bon.get(idx);
				c++;
				idx--;
			}
		}
		if(c==1)
		{
			c++;
			sb.append(0);
		}
		System.out.println(c);
		System.out.println(sb);

	}


}