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.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class WellknownNumbers {
    
    int s;
    long arr[];
    void run() {
        try {
            BufferedReader bfd = new BufferedReader(new InputStreamReader(
                    System.in));
            StringTokenizer tk = new StringTokenizer(bfd.readLine());
            s = Integer.parseInt(tk.nextToken());
            int k = Integer.parseInt(tk.nextToken()), i;
            arr = new long[100];
            arr[0] = 0;
            arr[1] = 1;
            arr[2] = 1;
            for(i = 3; i<arr.length; ++i) {
                if(i-k-1>=0) arr[i] = 2 * arr[i-1] - arr[i-k-1];
                else arr[i] = 2 * arr[i-1];
//              System.out.println(i+ " " +arr[i]);
                if(arr[i]>=1000000000) break;
            }
            ArrayList<Long> res = new ArrayList<Long>();
            int sum = s;
            while(sum>0) {
                if(arr[i]<=sum) {
                    sum-=arr[i];
                    res.add(arr[i]);
                }
                --i;
            }
            if(res.size()==1)
                res.add(0L);
            System.out.println(res.size());
            for(i = 0; i<res.size()-1; ++i)
                System.out.print(res.get(i)+" ");
            System.out.println(res.get(i));
            
        } catch (Exception e) {

        }
    }

    public static void main(String[] args) {
        new WellknownNumbers().run();
    }

}