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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;

public class Main {

  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter pw = new PrintWriter(System.out);

    String line = br.readLine();
    String[] split = line.split(" ");

    int s = Integer.parseInt(split[0]);
    int k = Integer.parseInt(split[1]);

    int n = 1;
    int[] kbonacciShifted = new int[1000000];
    kbonacciShifted[0] = 1;
    while (true) {
      for (int i = 1; i <= k && n - i >= 0; i++) {
        kbonacciShifted[n] += kbonacciShifted[n - i];
      }
      if (kbonacciShifted[n] >= s) {
        break;
      }
//      System.out.println(kbonacciShifted[n]);
      n++;
    }

    List<Integer> chosenList = new ArrayList<Integer>();

    for (int i = n; i >=0; i--) {
      if(s==0)break;
      if(s>=kbonacciShifted[i]){
        s-=kbonacciShifted[i];
        chosenList.add(kbonacciShifted[i]);
      }
    }

    if(chosenList.size()==1){
      chosenList.add(0);
    }

    pw.println(chosenList.size());

    for (Integer chosen : chosenList) {
      pw.print(chosen + " ");
    }

    pw.flush();
  }

}