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.*;

public class B implements Runnable {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer st;
	static Random rnd;

	void solve() throws IOException {
		int n = nextInt(), k = nextInt();
		
		ArrayList<Long> numbers  = new ArrayList<Long>();
		numbers.add(0L);
		numbers.add(1L);
		
		while(true) {
			long cur = 0;
			int canAdd = Math.min(k, numbers.size());
			
			for(int i = numbers.size() - 1; i >= numbers.size() - canAdd; i--)
				cur += numbers.get(i);
			
//			out.println(cur);
//			out.flush();
//			
//			out.println(cur);
//			out.flush();
			
			if(cur > n)
				break;
			
			numbers.add(cur);
		}
		
		ArrayList<Long> ans = new ArrayList<Long>();
		
		for(int i = numbers.size() - 1; i >= 0; i--) {
			long cur = numbers.get(i);
			
			if(n >= cur) {
				n -= cur;
				ans.add(cur);
			}
		}
		
		if(n != 0)
			throw new AssertionError();
		
		out.println(ans.size());
		
		for(int i = 0; i < ans.size(); i++) {
			out.print(ans.get(i));
			out.print((i + 1) == ans.size() ? "\n" : " ");
		}
	}

	public static void main(String[] args) {
		final boolean oldChecker = false;

		if (oldChecker)
			new Thread(null, new B(), "yarrr", 1 << 24).start();
		else
			new B().run();
	}

	public void run() {
		try {
			final String className = this.getClass().getName().toLowerCase();

			try {
				in = new BufferedReader(new FileReader(className + ".in"));
				out = new PrintWriter(new FileWriter(className + ".out"));
			} catch (FileNotFoundException e) {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			}

			rnd = new Random();

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(42);
		}
	}

	String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = in.readLine();

			if (line == null)
				return null;

			st = new StringTokenizer(line);
		}

		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());
	}
}