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.*;

public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(1, in, out);
        out.close();
    }

    static class Solver {
        int s, k;

        public void solve(int testNumber, InputReader in, PrintWriter out){
            s = in.nextInt();
            k = in.nextInt();
            long[] fib = new long[64];
            k = Math.min(k, 31);
            for (int i = 1; i < k; i++)
                fib[i] = 0;
            fib[k] = 1;
            for (int i = k + 1; i < fib.length; i++) {
                for (int j = i - k; j < i; j++)
                    fib[i] += fib[j];
            }
            ArrayList<Long> ans = new ArrayList<>();
            for (int i = fib.length-1; i > 0; i--) {
                if (fib[i] <= s) {
                    s -= fib[i];
                    ans.add(fib[i]);
                }
                if (s == 0)
                    break;
            }
            ans.add((long)0);
            out.println(ans.size());
            for (long i: ans)
                out.print(i + " ");
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() { return Long.parseLong(next()); }
    }
}