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 Codeforces {
	FastScanner in;
	PrintWriter out;

	void solve() {
		long s = in.nextLong();
		int k = in.nextInt();
		final int N = 100;
		long[] f = new long[N];
		f[0] = 1;
		int n = 1;
		for (int i = 1; i < N; i++) {
			f[i] = 0;
			for (int j = Math.max(0,  i - k); j < i; j++) {
				f[i] += f[j];
				if (f[i] > s) {
					n = i;
					break;
				}
			}
			if (f[i] > s) {
				break;
			}
		}
		ArrayList<Integer> ans = new ArrayList<Integer>();
		for (int i = n - 1; i >= 0; i--) {
			if (f[i] <= s) {
				ans.add(i);
				s -= f[i];
				
			}
		}
		out.println(ans.size() + 1);
		for (int x : ans) {
			out.print(f[x] + " ");
		}
		out.print(0);
	}

	void run() {
		in = new FastScanner();
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));

		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {

				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}

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