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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Locale;
import java.util.Queue;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class Solution implements Runnable {

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st;

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

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

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

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

	void solve() throws Exception {
		int n = nextInt();
		int k = nextInt();
		int[] a = new int[1000];
		a[0] = 0;
		a[1] = 1;
		int l = 2;
		for (l = 2; l < 1000;) {
			long r = 0;
			for (int j = 1; j <= k && l - j >= 0; j++) {
				r += a[l - j];
			}
			if (r > 1000000000) break;
			a[l++] = (int)r;
		}
		ArrayList<Integer> ans = new ArrayList<Integer>();
		while (n > 0) {
			while (l > 0 && a[l - 1] > n) l--;
			ans.add(a[l - 1]);
			n -= a[l - 1];
			l--;
		}
		if (ans.size() == 1) ans.add(0);
		out.println(ans.size());
		for (int i = 0; i < ans.size(); i++) out.print(ans.get(i) + " ");
	}

	public void run() {
		try {
			Locale.setDefault(Locale.UK);
			in = new BufferedReader(new InputStreamReader(System.in));
			// in = new BufferedReader(new FileReader("input.txt"));
			out = new PrintWriter(System.out);
			// out = new PrintWriter("output.txt");
			solve();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		} finally {
			out.close();
		}
	}

	public static void main(String[] args) {
		// new Thread(null, new Solution(), "1", 1 << 28).start();
		(new Solution()).run();
	}

}