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 Well_KnownNumbers {
    public static void main(String[] args) {
        Scanner cin = new Scanner(System.in);
        int s = cin.nextInt();
        int k = cin.nextInt();
        int f[] = new int[100000];
        int i = 1;
        f[0] = 1;
        int sum = 1;
        while (true) {
            f[i] += sum;
            if (f[i] >= s)
                break;
            if (i >= k)
                sum -= f[i - k];
            sum += f[i];
            i++;
        }
        ArrayList<Integer> ret = new ArrayList<Integer>();
        while (s > 0) {
            if (s - f[i] >= 0) {
                s -= f[i];
                ret.add(f[i]);
            }
            i--;
        }
        if (ret.size() == 1) {
            ret.add(0);
        }
        System.out.println(ret.size());
        for (int t : ret) {
            System.out.print(t + " ");
        }
        System.out.println();
        cin.close();
    }
}