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 Main {
	boolean eof;

	public String nextToken() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				eof = true;
				return "-1";
			}
		}
		return st.nextToken();
	}

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

	void solve() {
		int s = nextInt(), k = nextInt();
		long[] a = new long[200];
		a[0] = 1;
		a[1] = 1;
		a[2] = 2;
		int i;
		for (i = 3; i < 200 && a[i - 1] < s; ++i) {
			for (int j = 1; j <= k && i - j >= 0; ++j) {
				a[i] += a[i - j];
			}
		}
		ArrayList<Long> l = new ArrayList<Long>();
		for (; i >= 0 && s > 0; --i) {
			if (s - a[i] >= 0) {
				l.add(a[i]);
				s -= a[i];
				
			}
		}
		out.println(l.size());
		for (long x : l){
			out.print(x + " ");
		}
	}

	BufferedReader br;
	StringTokenizer st;
	PrintWriter out;

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

			// br = new BufferedReader(new FileReader("input.txt"));
			// out = new PrintWriter(new FileWriter("output.txt"));
			solve();
			br.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

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