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 Main {
    static long arr[];
    static int s;

    public static void main(String[] args) throws IOException {

        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(System.out);

        s = in.nextInt();
        int k = in.nextInt();
        Set<Long> st = new TreeSet();
        arr = new long[100];

        arr[0] = 1;

        st.add(1L);
        for (int i = k+1; arr[i-k-1]<s ; i++) {

            for (int j = 1; j <= k; j++) {
                if(i-j-k>=0) {
                    arr[i - k] += arr[i - j - k];
                }
                else
                    break;
            }
            st.add(arr[i-k]);
        }

        arr = new long[st.size()];
        int i=arr.length-1;
        for (Long val: st) {
            if(val!=0L)
            arr[i--] = val;

        }

        ArrayList<Long> result = new ArrayList();
        solve(0, 0, result);
        if(result.size()==1)
            result.add(0L);
        out.println(result.size());
        StringBuilder sb = new StringBuilder();
        for (int j = 0; j < result.size(); j++) {
            sb.append(result.get(j)+" ");
        }
        out.println(sb);

        out.close();

    }

    static boolean  solve(int i, long sum, ArrayList<Long> result){

        if(sum == s)return true;

        if(i>=arr.length || sum>s)return false;

        result.add(arr[i]);

        if(solve(i+1, sum+arr[i], result))
            return true;

        result.remove(result.size()-1);

        return solve(i+1, sum, result);
    }
    static class Comp implements Comparator<Long>{


        public int compare(Long x, Long y){
           if(x>y)return -1;
           return 1;
        }

    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

}