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.util.*;
public class Main {

    private void doit(){
        Scanner sc = new Scanner(System.in);
        while(sc.hasNext()){
            int s = sc.nextInt();
            int k = sc.nextInt();
            ArrayList<Long> list = new ArrayList<Long>();
            list.add((long)1);
            while(true){
                long sum = 0;
                for(int j = 1; j <= k && list.size() - j >= 0; j++){
                    sum+= list.get(list.size() - j);
                    //System.out.println("sum = " + sum);
                }
                if(sum > s) break;
                if(sum == s){
                    list.add(sum);
                    break;
                }
                list.add(sum);
            }

            int ans = 0;
            StringBuilder sb = new StringBuilder();
            long now = s;
            int len = list.size();
            for(int i =len - 1; i >= 0; i--){
                if(list.get(i) <= now){
                    now = now - list.get(i);
                    sb.append(" " + list.get(i));
                    ans++;
                }
                if(now == 0){
                    break;
                }
            }
            if(ans == 1){
                ans++;
                sb.append(" " + 0);
            }
            System.out.println(ans);
            System.out.println(sb.substring(1));

        }
    }

    public static void main(String [] args){
        new Main().doit();
    }
}