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 static java.lang.Math.*;
import static java.lang.Integer.parseInt;
import static java.lang.String.*;

public class Main {
	public static void main(String [] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		StringBuilder out = new StringBuilder();
		StringTokenizer tk;
		
		tk = new StringTokenizer(in.readLine());
		int s = parseInt(tk.nextToken()), k = parseInt(tk.nextToken());
		
		int [] fib = new int[1000];
		int cnt = 0;
		fib[cnt++] = 0;
		fib[cnt++] = 1;
		int i,tmp = 0;
		
		while(tmp < s) {
			for(i=cnt-1; i>=max(0,cnt-k); i--)
				fib[cnt] += fib[i];
			
			tmp += fib[cnt];
			cnt++;
		}
		
		int ans = 0;
		for(i=cnt-1; i>=0; i--) {
			if(fib[i] <= s) {
				s -= fib[i];
				if(ans>0) out.append(" ");
				out.append(fib[i]);
				ans++;
			}
		}
		
		System.out.println(ans);
		System.out.println(out);
	}
}