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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Solution {
	
	public class Point {
		int x, y;
		
		Point(int x, int y) {
			this.x = x;
			this.y = y;
		}
	}
	
	public class Pair {
		int a, b;
		
		Pair(int a, int b) {
			this.a = a;
			this.b = b;
		}
	}
	
	void solve() throws IOException {
		int s = nextInt(), k = nextInt(), sz = 0;
		int[] f = new int[100];
		ArrayList<Integer> ans = new ArrayList<Integer>(100);
		f[0] = 1;
		while (f[sz++] < s) {
			int sum = 0;
			for (int i = Math.max(0, sz - k); i < sz; ++i) {
				sum += f[i];
			}
			f[sz] = sum;
		}
		sz--;
		
		for (int i = sz; i >= 0 && s > 0; --i) {
			if (s >= f[i]) {
				s -= f[i];
				ans.add(f[i]);
			}
		}
		if (ans.size() == 1) {
			ans.add(0);
		}
		
		System.out.println(ans.size());
		for (int i = 0; i < ans.size(); ++i) {
			System.out.print(ans.get(i) + " ");
		}
	}

	BufferedReader br;
	StringTokenizer st;

	String next() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String s = br.readLine();
			if (s == null) {
				return "-1";
			}
			st = new StringTokenizer(s);
		}
		return st.nextToken();
	}

	int nextInt() throws IOException {
		return Integer.parseInt(next());

	}

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

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

	void run() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		solve();
		br.close();
	}

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

}