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.*;
import java.io.*;
public class cf
{
    static long brr[];
    static long arr[];
    public static void main(String[] args)
    {
        PrintWriter out= new PrintWriter(System.out);
        Scanner sc = new Scanner(System.in);
        int s=sc.nextInt();
        int k=sc.nextInt();
        int fib[]=new int[50];
        int counter=0;
        fib[0]=1;
        fib[1]=2;
        int sum=4;
        counter=2;
        while(sum<=s&&counter<k)
        {
            fib[counter++]=sum;
            sum*=2;
        }
        if(sum<=s)
        {
            sum-=1;
            fib[counter++]=sum;
        }
        sum*=2;
        sum-=1;
        int pointer=1;
        while(sum<=s)
        {
            fib[counter++]=sum;
            sum*=2;
            sum-=fib[pointer++];
        }
        int anscounter=0;
        int ans[]=new int[200];
        int i=counter-1;
        while(s!=0)
        {
            if(s>=fib[i])
            {
                s-=fib[i];
                ans[anscounter++]=fib[i];
            }
            i--;
        }
        if(anscounter==1)
        {
            ans[anscounter++]=0;
        }
        System.out.println(anscounter);
        
        for(int i1 = 0 ;i1<anscounter;i1++)
        System.out.print(ans[i1]+" ");
    }
}