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.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class Main {
    static void zap() throws IOException {
        int s = nextInt();
        int k = nextInt();
        int[] arr = new int[102];
        arr[0] = arr[1] = 1;
        int sumSoFar = 2, tail = 0, i;
        for(i=2;i<=101;i++)
        {
            if(i - tail < k)
            {
                arr[i] = sumSoFar;
                sumSoFar <<= 1;
            }
            else if(i - tail == k)
            {
                arr[i] = sumSoFar;
                sumSoFar = (sumSoFar << 1) - arr[tail];
                tail++;
            }
            if(arr[i] >= (int)1e9)
                break;
        }
        List<Integer> lst = new ArrayList<Integer>();
        int r = i;
        while(1 <= r && s > 0)
        {
            if(arr[r] <= s)
            {
                s -= arr[r];
                lst.add(arr[r]);
            }
            r--;
        }
        lst.add(0);
        out.println(lst.size());
        for(int num : lst)
            out.print(num + " ");
    }

    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter out;

    public static void main(String[] args) throws IOException {
        InputStream input = System.in;
        OutputStream output = System.out;
        br = new BufferedReader(new InputStreamReader(input));
        out = new PrintWriter(output);
        zap();
        out.close();
    }

    static long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    static String nextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = br.readLine();
            if (line == null) {
                return null;
            }
            st = new StringTokenizer(line);
        }
        return st.nextToken();
    }
}