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.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.*;


public class B
{
    BufferedReader in;
    PrintStream out;
    StringTokenizer tok;
    public B() throws NumberFormatException, IOException
    {
        in = new BufferedReader(new InputStreamReader(System.in));
        //in = new BufferedReader(new FileReader("in.txt"));
        out = System.out;
        run();
    }
    
    void run() throws NumberFormatException, IOException
    {
        int s = nextInt();
        int k = nextInt();
        List<Long> fib = new ArrayList<Long>();
        fib.add(1L);
        long a  = 1;
        while(a < 1000000000)
        {
            fib.add(a);
            if(fib.size()>k)
                a = 2*a-fib.get(fib.size()-1-k);
            else a = 2*a;
        }
        List<Long> ans = new ArrayList<Long>();
        while(s>0)
        {
            int i = 1;
            while(i < fib.size() && fib.get(i) < s)
                i++;
            if( !(i < fib.size() && fib.get(i) == s) )
            i--;
            s-=fib.get(i);
            ans.add(fib.get(i));
        }
        if(ans.size()==0)
        {
            out.println(1);
            out.println(0);
        }
        else if(ans.size()==1)
        {
            out.println(2);
            out.println("0 " + ans.get(0));
        }
        else
        {
            out.println(ans.size());
            out.print(ans.get(0));
            for(int i = 1; i < ans.size(); i++)
                out.print(" " + ans.get(i));
            out.println();
        }
    }
    public static void main(String[] args) throws NumberFormatException, IOException 
    {
        new B();
    }
    String nextToken() throws IOException
    {
        if(tok ==null || !tok.hasMoreTokens()) tok = new StringTokenizer(in.readLine());
        return tok.nextToken();
    }
    int nextInt() throws NumberFormatException, IOException
    {
        return Integer.parseInt(nextToken());
    }
    long nextLong() throws NumberFormatException, IOException
    {
        return Long.parseLong(nextToken());
    }
    double nextDouble() throws NumberFormatException, IOException
    {
        return Double.parseDouble(nextToken());
    }
}