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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Map.Entry;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.Vector;
 
 
public class Main {
	public static void main(String[] args) throws IOException{
		  	FastScanner sc = new FastScanner();
			PrintWriter out = new PrintWriter(System.out);
			int s = sc.nextInt();
			int k =sc.nextInt();
			k =Math.min(k, 30);
			Long a[]= new Long[50];
			a[0]=0L;
			a[1]=0L;
			a[2]=1L;
			for(int i=3;i<=49;i++){
				long sum =0L;
				int j=i-1;
				for(int l=1;l<=k;l++)sum+=a[Math.max(0, j--)];
				a[i]=sum;
			}
			ArrayList<Long>arr = new ArrayList<Long>();
			arr.add(0L);
			Arrays.sort(a);
			Long suuu = 0L;
			for(int i=49;i>=2;i--){
				if(s==0)break;
				if(a[i]<=s){
					suuu+=a[i];
					s-=a[i];
					arr.add(a[i]);
				}
				if(s==0)break;
			}
			System.out.println(arr.size());
			for(Long i:arr){
				out.print(i+" ");
			}
			//System.out.println(suuu);
	out.close();
		
			
			
			
	}


			

			
			
			
	
	



	
	
			    
			


			
			
	
	
	

			
	
		
	
	
	
		

			

		

	
	

	
	
	

			
						
			

	
	

		
		
		





















































	static void generate(int[] p, int L, int R) {
		  if (L == R) {
		      
		      
		  }else { 
		    for (int i = L; i <= R; i++) {
		    	int tmp = p[L]; p[L] = p[i]; p[i] = tmp;//swap
		      generate(p, L+1, R);//recurse 
		      tmp = p[L]; p[L] = p[i]; p[i] = tmp;//unswap

		    }
		  }
		}
	
}
		 


	
	
	
	











	
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
class FastScanner {
 
 
 
 
    BufferedReader br;
    StringTokenizer st;
 
    public FastScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
 
    public FastScanner(String s) {
        try {
            br = new BufferedReader(new FileReader(s));
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }
 
    String nextToken() {
        while (st == null || !st.hasMoreElements()) {
            try {
 
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    int nextInt() {
        return Integer.parseInt(nextToken());
    }
 
    long nextLong() {
        return Long.parseLong(nextToken());
    }
 
    double nextDouble() {
        return Double.parseDouble(nextToken());
    }
 
 
}