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.*;

public class A{
    public static void main(String args[]){
        Scanner in = new Scanner(System.in);
        long s = in.nextLong();
        long k = in.nextLong();
        ArrayList<Integer> arr = new ArrayList<>();
        int x=1;
//        if(s==1)
//        {
//            System.out.println("2");
//            System.out.println("0 1");
//            return;
//        }
        arr.add(1);
        int index = 0;
        while(x<=s){
//            System.out.println(x);
            arr.add(x);
            if(x==s)
                break;
            x+=x;
            if(arr.size()>k){
                x-=arr.get(index);
                index++;
            }
                
        }
        if(s==x)
        {
            System.out.println("2");
            System.out.println("0 "+x);
            return;
        }
        int n = arr.size();
        ArrayList<Integer> ans = new ArrayList<>();
        long sum=0;
        for(int i=n-1;i>=0;i--){
            if(sum+arr.get(i)<=s){
                sum+=arr.get(i);
                ans.add(arr.get(i));
                if(sum==s)
                    break;
            }
        }
        n = ans.size();
        System.out.println(n);
        for(int z:ans){
            System.out.print(z+" ");
        }
    }
}