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.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

public class B {
	static BufferedReader in;
	static StringTokenizer st;
	static PrintWriter out;
	
	static String nextToken() throws IOException {
		while (!st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}
	
	static int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(nextToken());
	}
	static int f[];
	public static void main(String[] args) throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		st = new StringTokenizer(in.readLine());
		out = new PrintWriter(new OutputStreamWriter(System.out));
		int s = nextInt();
		int k = nextInt();
		f = new int [101];
		f[0] = 0;
		f[1] = 1;
		int size = 0;
		for (int i = 2; i <=100; i++) {
			for (int j = 1; j <= k; j++) {
				if(i-j > 0){
					f[i] += f[i-j];
					
				}else{
					break;
				}
			}
			if(f[i]< 0 || f[i] > s){
				size = i-1;
				break;
			}
//			System.out.print(f[i]+" ");
		}
		String ans = "";
		int m = 0;
		for (int i = size; i >=1; i--) {
			if(s >= f[i]){
				m++;
				ans += f[i]+" ";
//				System.out.println(ans);
				s-=f[i];
			}
		}
		if(m==1){
			m++; 
			ans += "0";
		}
		System.out.println(m);
		System.out.println(ans);
	}
}