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.*;
import java.math.BigInteger;
import java.util.*;


public class B
{
        String line;
        StringTokenizer inputParser;
        BufferedReader is;
        FileInputStream fstream;
        DataInputStream in;
        String FInput="";
        
        void openInput(String file)
        {

                if(file==null)is = new BufferedReader(new InputStreamReader(System.in));//stdin
                else
                {
                        try{
                
                                
                        fstream = new FileInputStream(file);
                        in = new DataInputStream(fstream);
                        is = new BufferedReader(new InputStreamReader(in));
                        }catch(Exception e)
                        {
                                System.err.println(e);
                        }
                }

        }
        
        void readNextLine()
    	{
    		try {
    			line = is.readLine();
    			inputParser = new StringTokenizer(line, " ");
    			//System.err.println("Input: " + line);
    		} catch (IOException e) {
    			System.err.println("Unexpected IO ERROR: " + e);
    		}	
    		catch (NullPointerException e)
    		{
    			line=null;
    			
    		}
    		
    	}
        
        long NextLong()
        {
                String n = inputParser.nextToken();
                
                long val = Long.parseLong(n);
                
                 return val;
        }
        
        int NextInt()
        {
                String n = inputParser.nextToken();
                int val = Integer.parseInt(n);
                
                //System.out.println("I read this number: " + val);
                return val;
        }
        
        String NextString()
        {
                String n = inputParser.nextToken();
                return n;
        }
        
        void closeInput()
        {
                try {
                        is.close();
                } catch (IOException e) {
                        System.err.println("Unexpected IO ERROR: " + e);
                }
                        
        }
        
        
        public static void main(String [] argv)
        {
                String filePath=null;
                if(argv.length>0)filePath=argv[0];
                new B(filePath);
        }
        
        public void readFInput()
    	{
    		for(;;)
    		{
    			try
    			{
    				readNextLine();
    				FInput+=line+" ";
    			}
    			catch(Exception e)
    			{
    				break;
    			}
    		}
    		inputParser = new StringTokenizer(FInput, " ");
    	}
        
        int [] an;
       
        public B(String inputFile)
        {
        	openInput(inputFile);
        	
        	readNextLine();
    		
    		int n=NextInt(),k=NextInt();
    		

    		an = new int[50];
    		int anCnt=0;
    		
    		long s=1;
    		int i=0;
        	while(s<=1000000000)
        	{	
        		an[anCnt++]=(int) s;
        		if(i>0)s+=s;
        		if(i>=k)s-=an[i-k];
        		i++;
        	}
        	
        	int cnt=1;
        	String out="0 ";
        	
    		for(int j=anCnt-1; j>=0; j--)
    		{
    			if(n>=an[j])
    			{
    				cnt++;
    				out+=an[j]+" ";
    				n-=an[j];
    			}
    		}

        	
        	
        	
        	System.out.println(cnt);
        	System.out.println(out);
        	
        	
        	
    		
            closeInput();		
    	}
        
        
       
       
}