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 java.math.*;

public class Main {
    static StringTokenizer st;
    static PrintWriter out = new PrintWriter(System.out,true);
    static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));

    public static int nextInt() throws Exception {
        if(st == null || !st.hasMoreTokens()) st = new StringTokenizer(in.readLine());
        return Integer.parseInt(st.nextToken());
    }

    public static void main(String[] args) throws Exception {
        int s = nextInt();
        int k = nextInt();
        ArrayList<Integer> list = new ArrayList<>();
        list.add(1);
        list.add(1);
        list.add(2);
        while(list.get(list.size()-1) <= s) {
            int tmp = 0;
            for(int i = 0;i < k && list.size()-i-1 >= 0;i++) {
                tmp += list.get(list.size()-i-1);
            }
            list.add(tmp);
        }
        list.remove(list.size()-1);
        //out.println(list.toString());
        ArrayList<Integer> ans = new ArrayList<>();
        for(int i = list.size()-1;i >= 0;i--) {
            if(s - list.get(i) >= 0 ) {
                ans.add(list.get(i));
                s -= list.get(i);
            }
        }
        if(ans.size() == 1) out.println(2);
        else out.println(ans.size());
        for(int a : ans) out.print(a+" ");
        if(ans.size() == 1) out.print("0 ");
        out.println();
    }
}