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.*;

public class WellKnownNumbers {
    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(f.readLine());
        int s = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        int[] a = new int[100];
        a[0] = 1;
        int index = 1;
        int x = 0;
        for (int i = Math.max(0, index-k); i < index; i++)
            x += a[i];
        while (x <= 1000000000)
        {
            a[index++] = x; 
            x = 0;
            for (int i = Math.max(0, index-k); i < index; i++)
                x += a[i];
        }
        int[] b = new int[100];
        index--;
        int index2 = 0;
        while (s > 0)
        {
            while (a[index] > s)
                index--;
            b[index2++] = a[index];
            s -= a[index];
        }
        b[index2++] = 0;
        System.out.println(index2);
        for (int i = 0; i < index2; i++)
            System.out.print(b[i]+" ");
        System.out.println();
    }
}