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.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class E {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        // Scanner scan = new Scanner(System.in);
        // PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out)); 
        // int n = Integer.parseInt(bf.readLine());
        StringTokenizer st = new StringTokenizer(bf.readLine());
        // int[] a = new int[n]; for(int i=0; i<n; i++) a[i] = Integer.parseInt(st.nextToken());
        int s = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        long[] vals = new long[45];
        vals[0] = 1;
        vals[1] = 1;
        int cap = 0;
        for(int i=2; i<=45; i++) {
            if(i-1-k < 0) vals[i] = 2*vals[i-1];
            else vals[i] = 2*vals[i-1] - vals[i-1-k];
            if(vals[i] > s) {
                cap = i;
                break;
            }
        }
        ArrayList<Integer> ans = new ArrayList<Integer>();
        ans.add(0);
        int cur = s;
       //System.out.println(Arrays.toString(vals));
        for(int i=cap-1; i>=1; i--) {
            if((int)vals[i] <= cur) {
                cur -= (int)vals[i];
                ans.add((int)vals[i]);
            }
        }
        System.out.println(ans.size());
        for(int i : ans) System.out.print(i + " ");
        //System.out.print("\n"+cur);
        // int n = scan.nextInt();
        
        // out.close(); System.exit(0);
    }
}