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 cf225b {
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    long s = in.nextInt();
    int k = in.nextInt();
    long[] v = new long[1000];
    v[0] = 1;
    TreeSet<Long> vals = new TreeSet<Long>();
    for(int i=1; i<1000; i++) {
      for(int j=1; j<=k; j++)
        if(i-j >= 0)
          v[i] += v[i-j];
        else 
          break;
      if(v[i] > s) break;
      vals.add(v[i]);
    }
    ArrayList<Long> ans = new ArrayList<Long>();
    while(s > 0) {
      ans.add(vals.lower(s+1));
      s -= vals.lower(s+1);
    }
    if(ans.size() < 2) ans.add(0L);
    System.out.println(ans.size());
    for(long x : ans)
      System.out.print(x+" ");
  }
}