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.ArrayList;
import java.util.Scanner;

public class B_225_Well_known_Numbers {
	public static void main(String[] args){
		  Scanner in = new Scanner(System.in);
		    int s = in.nextInt();
		    int k = in.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++;
		    }
		    /*
		    for(int j=0;f[j]!=0;j++)
		      System.out.print(f[j] + " ");
		    System.out.println();
		    */
		    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();

	}
}