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.StringTokenizer;

public class Ans
{
    static BufferedReader br ;
    static PrintWriter out ;
    static StringTokenizer tok ;
    static String next() throws IOException
    {
        while(!tok.hasMoreTokens())
        {
            tok = new StringTokenizer( br.readLine());
        }
        return tok.nextToken();
    }
    static int nextInt() throws IOException , NumberFormatException
    {
        return Integer.parseInt(next());
    }

    public static void main(String[] args) throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));
        tok = new StringTokenizer(br.readLine());
        out=new PrintWriter(new OutputStreamWriter(System.out));
        int s = nextInt();
        int k = nextInt();
        int ans[] = new int[101];
        ans[0]=0;
        ans[1]=1;
        int size =0;
        for(int i = 2 ; i <=100 ; i++)
        {
            for(int j = 1 ; j <= k ; j++)
            {
                if(i-j>0)
                {
                    ans[i]+=ans[i-j];
                }
                else
                {
                        break ;
                }
            }
            if (ans[i] < 0 || ans[i] > s ) {
                size = i-1;
                break ;
            }
        }
        String ans_1 = "";
        int m =0;
        for(int i = size ; i>=1 ; i--)
        {
            if( s >= ans[i])
            {
                m++;
                ans_1+=ans[i]+" ";
                s-=ans[i];
            }

        }
        if( m == 1)
        {
            m++;
            ans_1+="0";
        }
        out.println(m);
        out.println(ans_1);
    br.close();
    out.close();
    }
}