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 All {
	public static void main(String[] args) throws IOException {
		BufferedReader rd = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(rd.readLine());
		int s = Integer.parseInt(st.nextToken()), k = Integer.parseInt(st.nextToken());
		if(k>33){
			String bin = Integer.toBinaryString(s);
			ArrayList<Integer> ans = new ArrayList<Integer>();
			for(int i=0; i<bin.length(); i++){
				int curDigit = bin.charAt(i)=='0'? 0: 1, ind = bin.length()-1-i;
				if(curDigit==1) ans.add(1<<ind);
			}
			if(ans.size()==1) ans.add(0);
			pw.println(ans.size());
			for(int i=0; i<ans.size(); i++) pw.print(ans.get(i)+" ");
			pw.println();
			pw.flush();
		}
		else{
			long[] a = new long[100];
			a[k] = 1;
			for(int i=k+1; i<a.length; i++){
				long sum = 0;
				for(int j=i-1; j>=i-k; j--) sum += a[j];
				a[i] = sum;
			}
			int first = 0;
			for(int i=0; i<a.length; i++) if(a[i]>1000000000){ first = i; break; }
			ArrayList<Integer> ans = new ArrayList<Integer>();
			recursiveRepr(s, ans, a, true, first);
			ans.add(0);
			pw.println(ans.size());
			for(int i=0; i<ans.size(); i++) pw.print(ans.get(i)+" ");
			pw.println();
			pw.flush();
		}
	}
	
	static void recursiveRepr(int num, ArrayList<Integer> list, long[] a, boolean first, int max){
		if(num==0){
			return;
		}
		for(int i=max; i>=0; i--) if(a[i]<=num){
		//	if(first && a[i]==num) continue;
			list.add((int)a[i]);
			recursiveRepr((int) (num-a[i]), list, a, false, max);
			return;
		}
	}
	
}