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.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

public class B {
    
    void run(){
        Scanner sc = new Scanner(System.in);
        int S = sc.nextInt(), K = sc.nextInt();
        List<Integer> res = new ArrayList<Integer>();
        res.add(0);
        if(32 <= K){
            int x = 1<<30;
            while(S>0){
                if(x <= S){
                    S-=x;
                    res.add(x);
                }
                x>>=1;
            }
        }
        else{
            List<Integer> list = new ArrayList<Integer>();
            list.add(1);
            for(;;){
                int x = 0;
                for(int i=list.size()-1;i>=list.size()-K&&i>=0;i--){
                    x+=list.get(i);
                    if(S < x)break;
                }
                if(S < x)break;
                list.add(x);
            }
            for(int i=list.size()-1;i>=0;i--){
                int x = list.get(i);
                if(x <= S){
                    S-=x; res.add(x);
                }
                if(S==0)break;
            }
        }
        int m = res.size();
        System.out.println(m);
        for(int i=0;i<m;i++)System.out.print(res.get(i)+(i==m-1?"\n":" "));
    }
    
    void debug(Object...o){
        System.out.println(Arrays.deepToString(o));
    }
    
    public static void main(String[] args) {
        new B().run();
    }
}