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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class B {

    static Scanner in = new Scanner(System.in);

    public static void main(String[] args) {
        int s = in.nextInt(), k = in.nextInt();
        List<Integer> l = new ArrayList<Integer>(), sum = new ArrayList<Integer>();
        l.add(0);
        l.add(1);
        sum.add(0);
        sum.add(1);
        for (int i = 2;; i++) {
            int j = Math.max(i - k - 1, 0);
            int cur = sum.get(i - 1) - sum.get(j);
            l.add(cur);
            sum.add(sum.get(i-1) + cur);
            if(sum.get(i) > 1000000000)
                break;
        }
        
        List<Integer> res = new ArrayList<Integer>();
        for(int i = l.size() - 1; s >= 0 && i >= 0; i--) {
            if(l.get(i) <= s) {
                res.add(l.get(i));
                s -= l.get(i);
            }
        }
        System.out.println(res.size());
        for(int i = 0 ; i < res.size(); i++)
            System.out.print(res.get(i) + " ");
        System.out.println();
    }

}