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.Collections;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class B {

    List<Integer> list = new ArrayList<Integer>();
    boolean[] u;
    int n, S, K;
    
    boolean f(int k, int use, int sum){
        if(sum == S){
            if(2<=use)return true;
        }
        if(k==-1 || S < sum){
            return false;
        }
        u[k] = true;
        if(f(k-1, use+1, sum+list.get(k)))return true;
        u[k] = false;
        return f(k-1, use, sum);
    }
    
    void run(){
        Scanner sc = new Scanner(System.in);
        S = sc.nextInt(); K = sc.nextInt();
        list.add(0);
        list.add(1);
        Set<Integer> cand = new HashSet<Integer>();
        cand.add(0); cand.add(1);
        for(;;){
            long sum = 0;
            if(list.size()>K)list.remove(0);
            for(int x:list)sum+=x;
            if(S<sum)break;
            list.add((int)sum);
            cand.add((int)sum);
        }
        n = cand.size();
        list.clear();
        for(int x:cand)list.add(x);
        Collections.sort(list);
        u = new boolean[n];
        f(n-1, 0, 0);
        int m = 0;
        List<Integer> res = new ArrayList<Integer>();
        for(int i=0;i<n;i++)if(u[i]){
            m++;
            res.add(list.get(i));
        }
        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();
    }
}