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 static java.lang.Math.*;

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class aa{
	static long s, sum[], nums[];
	static int k, from = 0;

	static void get() {
		s = nextLong();
		k = nextInt();
		sum = new long[1000];
		nums = new long[1000];
		sum[1] = 1;
		nums[1] = 1;

		for (int i = 2; i < sum.length; i++) {
			if (k >= i) {
				nums[i] = sum[i - 1];
			} else {
				nums[i] = sum[i - 1] - sum[i - 1 - k];
			}
			sum[i] = sum[i - 1] + nums[i];
			from = i;
			if (nums[i] >= s)
				break;
		}
	}

	public static void solve() {
		get();

		ArrayList<Long> ans = new ArrayList<Long>();
		for (int i = from; i > 1; i--) {
			if (sum[i - 1] <= s) {
				s -= nums[i];
				ans.add(nums[i]);
			}
		}
		ans.add(0l);
		out.println(ans.size());
		for (int i = ans.size() - 1; i >= 0; i--) {
			out.print(ans.get(i));
			out.print(" ");
		}
		out.flush();
		// --------------------------------------------------------------------------------------------
		out.close();
		System.exit(0);
	}

	private static boolean fileIOMode = false;
	private static String problemName = "yyy";

	private static BufferedReader in;
	private static PrintWriter out;
	private static StringTokenizer tokenizer;

	public static void main(String[] args) throws Exception {
		if (fileIOMode) {
			in = new BufferedReader(new FileReader(problemName + ".in"));
			out = new PrintWriter(problemName + ".out");
		} else {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
		}
		tokenizer = new StringTokenizer("");

		solve();
	}

	private static String nextLine() {
		try {
			return in.readLine();
		} catch (IOException e) {
			return null;
		}
	}

	private static String nextToken() {
		while (!tokenizer.hasMoreTokens()) {
			tokenizer = new StringTokenizer(nextLine());
		}
		return tokenizer.nextToken();
	}

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

	private static long nextLong() {
		return Long.parseLong(nextToken());
	}

	private static double nextDouble() {
		return Double.parseDouble(nextToken());
	}

	private static BigInteger nextBigInteger() {
		return new BigInteger(nextToken());
	}

	private static void print(Object o) {
		if (fileIOMode) {
			System.out.print(o);
		}
		out.print(o);
	}

	private static void println(Object o) {
		if (fileIOMode) {
			System.out.println(o);
		}
		out.println(o);
	}

	private static void printf(String s, Object... o) {
		if (fileIOMode) {
			System.out.printf(s, o);
		}
		out.printf(s, o);
	}
}