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 Solve{
    public static void main(String[] args){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int k=sc.nextInt();
        int[] fib=new int[1000000];
        fib[0]=0;
        fib[1]=1;
        int start=1;
        int pos=0;
        while(true){
            if(fib[start]>=n){
                pos=start;
                break;
            }
            start++;
            for(int j=Math.max(1,start-k);j<start;j++){
                fib[start]+=fib[j];
            }
        }
        ArrayList<Integer> al=new ArrayList<>();
        al.add(0);
        for(int i=pos;i>=1;i--){
            if(n>=fib[i]){
                n-=fib[i];
                al.add(fib[i]);
            }
            if(n==0)break;
        }
        System.out.println(al.size());
        for(int a:al)System.out.print(a+" ");
        
    }
}