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 C139B
{

    private static StringTokenizer st;
    
    public static void nextLine(BufferedReader br) throws IOException
    {
        st = new StringTokenizer(br.readLine());
    }
    
    public static int nextInt()
    {
        return Integer.parseInt(st.nextToken());
    }
    
    public static String next()
    {
        return st.nextToken();
    }
    
    public static long nextLong()
    {
        return Long.parseLong(st.nextToken());
    }
    
    static long MAX = 1000000000;
    /**
     * @param args
     */
    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        nextLine(br);
        long s = nextLong();
        long k = nextLong();
        long[] fib = new long[1000];
        fib[0] = 0;
        fib[1] = 1;
        int count = 1;
        for (int i = 2; i < 1000; i++)
        {
            long sum = 0;
            for (int j = i - 1; j >= Math.max(0, i-k); j--)
            {
                sum += fib[j];
            }
            if (sum > MAX)
            {
                break;
            }
            fib[i] = sum;
            count = i;
        }
        ArrayList<Long> list = new ArrayList<Long>();
        for (int i = 0; i <= count; i++)
        {
            if (!list.contains(fib[i]))
            {
                list.add(fib[i]);
            }
        }
        int ptr = list.size() - 1;
        ArrayList<Long> ans = new ArrayList<Long>();
        while (s > 0 && ptr > 0)
        {
            if (list.get(ptr) <= s)
            {
                ans.add(list.get(ptr));
                s -= list.get(ptr);
            }
            else
            {
                ptr--;
            }
        }
        if (ans.size() == 1)
        {
            ans.add(new Long(0));
        }
        System.out.println(ans.size());
        for (int i = 0; i < ans.size(); i++)
        {
            System.out.print(ans.get(i));
            if (i != ans.size() - 1) System.out.print(" ");
        }
        System.out.println();
    }
    
}