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 BR139 {
	BufferedReader in;
	PrintWriter out;
	StringTokenizer st;
	
	final int MaxN = 10000000;

	void solve() throws IOException {
		int s = nextInt(), k = nextInt();
		
		int[] a = new int[MaxN];
		a[0] = 1;
		a[1] = 1;
		a[2] = 2;
		int id = 1;
		for (int i = 1; a[i - 1] < s; i++){
			id = i;
			int t = 0;
			for (int j = i - 1; i - j <= k && j >= 0; j--)
				t += a[j];
			a[i] = t;
			//if (a[i] >= MaxN - a[i])
			//	break;					
		}
		//for (int i = 0; a[i] < s; i++)
		//	out.print(a[i]);
		boolean f = false;
		int[] res = new int[MaxN];
		int count = 0;
		for (int i = id; i > 0; i--){	
			if (s - a[i] == 0 && !f){
				res[count] = a[i];
				count++;
				res[count] = 0;
				count++;
				s = s - a[i];
				f = true;
			}
			if (s - a[i] >= 0){
				res[count] = a[i];
				count++;
				//out.print(a[i] + " ");
				s = s - a[i];
				f = true;
			}
		}
		out.println(count);
		for (int i = 0; i < count; i++)
			out.print(res[i] + " ");
	}

	void run() throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(new OutputStreamWriter(System.out));

		solve();

		in.close();
		out.close();
	}

	public static void main(String[] args) throws IOException {
		new BR139().run();
	}

	String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}

}