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 b {
public static void main(String[] args)
{
    Scanner input = new Scanner(System.in);
    int s = input.nextInt(), k = input.nextInt();
    ArrayList<Long> data = new ArrayList<Long>();
    data.add(1l);
    while(true)
    {
        long next = 0;
        for(int i = data.size()-1; i>= 0 && i >= data.size()-k; i--)
            next += data.get(i);
        if(next > 1e9)
            break;
        data.add(next);
    }
//  for(int i = 0; i<data.size(); i++)
//      System.out.println(data.get(i));
    long sum = 0;
    int n = data.size();
    ArrayList<Long> used = new ArrayList<Long>();
    for(int i = n-1; i>=0; i--)
    {
        long needed = s - sum;
        if(data.get(i) <= needed)
        {
            sum += data.get(i);
            used.add(data.get(i));
        }
            
    }
    if(used.size() ==1)
        used.add(0l);
    Collections.sort(used);
    System.out.println(used.size());
    for(int i = 0; i<used.size()-1; i++)
        System.out.print(used.get(i) + " ");
    System.out.println(used.get(used.size()-1));
}
}