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.*;
import java.math.*;
import java.awt.geom.*;

import static java.lang.Math.*;

public class Solution implements Runnable {
	
	public void solve () throws Exception {
		long s = nextLong();
		int k = nextInt();
		ArrayList<Long> fib = new ArrayList<>();
		fib.add(1L);
		for (int i = 0; ; i++) {
			long num = 0;
			for (int j = fib.size() - 1; j >= fib.size() - k && j >= 0; j--) {
				num += fib.get(j);
			}
			if (num > s) break;
			fib.add(num);
		}
		ArrayList<Long> answer = new ArrayList<Long>();
		for (int j = fib.size() - 1; j >= 0; j--) {
			if (s - fib.get(j) >= 0) {
				s -= fib.get(j);
				answer.add(fib.get(j));
			}
		}
		if (answer.size() == 1) {
			answer.add(0L);
		}
		out.println(answer.size());
		for (int i = 0; i < answer.size(); i++) {
			out.print(answer.get(i)+" ");
		}
	}
	
	private static long stime = 0;
	
	private BufferedReader in;
	private PrintWriter out;
	private StringTokenizer st;
	
	private String nextToken () throws Exception {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}
	
	private int nextInt () throws Exception {
		return Integer.parseInt(nextToken());
	}
	
	private long nextLong () throws Exception {
		return Long.parseLong(nextToken());
	}
	
	private double nextDouble () throws Exception {
		return Double.parseDouble(nextToken());
	}
	
	@Override
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(new OutputStreamWriter(System.out));
			
			solve ();
		} catch (Exception e) {
			throw new RuntimeException(e);
		} finally {
			out.close();
		}
	}
	
	public static void main(String[] args) {
		new Thread(null, new Solution(), "", 1<<26).start();
	}

}