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.IOException;
import java.io.InputStreamReader;
import java.io.StreamTokenizer;
import java.util.ArrayList;


public class B {
    static InputStreamReader in = new InputStreamReader(System.in);
    static BufferedReader bf = new BufferedReader(in);
    static StreamTokenizer st = new StreamTokenizer(bf);
    public static void main(String[] args) throws IOException{
        int s = nextInt();
        int k = nextInt();  
        int []a = new int [45];
        a[1] = 1;
        boolean f = true;
        for (int i = 2; i <=44; i++) {
            if (k > i){
                for (int j = 0; j < i; j++) {
                    a[i] +=a[j];
                    if (a[i] < 0){
                        a[i] = 0;
                        f = false;
                        break;
                    }
                }
            }else{
                for (int j = i-k; j < i; j++) {
                    a[i] +=a[j];
                    if (a[i] < 0){
                        a[i] = 0;
                        f = false;
                        break;
                    }
                }
            }
            if (!f){
                break;
            }
        }
        ArrayList<Integer> ans = new ArrayList<Integer>();
        while (s !=0){
        for (int i = 44; i >=2; i--) {
            if (s >=a[i] && a[i] != 0){
                ans.add(a[i]);
                s -= a[i];
            }
        }
        }
        if (ans.size() ==1){
            ans.add(0);
        }
        System.out.println(ans.size());
    for (Integer v : ans) {
        System.out.print(v+" ");
    }
    }
    private static String next() throws IOException{
        st.nextToken();
        return st.sval;
    }
    private static int nextInt() throws IOException{
        st.nextToken();
        return (int) st.nval;
    }

}