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.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;


public class Main {
    static ArrayList<ArrayList<Integer>> ar ;
    static boolean chk(pair p1 , pair p2){
        boolean test1 = p2.a < p1.a && p1.a < p2.b ;
        boolean test2 = p2.a < p1.b && p1.b < p2.b ;

        return test1 || test2 ;
    }
    static boolean dfs(boolean vi[] , int num , int target){
        if(num == target)
            return true ;
        boolean flag = false ;
        for(int i = 0 , n = ar.get(num).size(); i < n ; i++){
            int x = ar.get(num).get(i) ;
            if(!vi[x]){
                vi[x] = true ;
                flag = flag || dfs(vi , x , target) ;
            }
        }
        return flag ;

    }
    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        StringBuilder ans = new StringBuilder();
        int sum = Reader.nextInt() ;
        int k = Reader.nextInt() ;
        long ar[] = new long[50] ;
        ar[0] = 0 ;
        ar[1] = 1 ;
        ar[2] = 1 ;
        for(int i = 3 ;i< 50 ; i++){
            for(int j = 1  ;  j <= k && i-j >= 0; j++)
             ar[i] += ar[i-j]  ;
        }
        int c = 1 ;
        for(int i = ar.length - 1 ; i > 1 ; i--){
            if(sum >= ar[i]) {
                sum -= ar[i];
                ans.append(ar[i]+" ") ;
                c++ ;
            }
        }

        ans.append("0") ;
        System.out.println(c);
        System.out.print(ans);



    }






}

class pair{
    int a , b ;
    pair(int a , int b ){
        this.a = a ;
        this.b = b ;
    }
}
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;


    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }


    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {

            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static int nextShort() throws IOException {
        return Short.parseShort(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}