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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Yury Bandarchuk
 */
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);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }

    static class Task {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            long s = in.nextLong();
            int k = in.nextInt();
            if (k > 100) {
                out.println(Long.bitCount(s) + 1);
                for (long i = 0L; i < 60L; i++) {
                    if ((s & (1L << i)) != 0L) {
                        out.print((1L << i) + " ");
                    }
                }
                out.println("0");
                return;
            }
            long[] fib = new long[2000];
            for (int i = 0; i < k; i++) {
                fib[i] = 0L;
            }
            fib[k] = 1L;
            int sz = 0;
            for (int i = k + 1; i < 2000; i++) {
                fib[i] = 0L;
                for (int j = i - k; j < i; j++) {
                    fib[i] += fib[j];
                    if (fib[i] >= s) {
                        break;
                    }
                }
                if (fib[i] >= s) {
                    sz = i;
                    break;
                }
            }
            if (fib[sz] == s) {
                out.println(2);
                out.println(fib[sz] + " 0");
                return;
            }
            ArrayList<Long> result = new ArrayList<>();
            for (int i = sz - 1; i >= 0; --i) {
                if (s - fib[i] >= 0L && fib[i] > 0L && !result.contains(fib[i])) {
                    result.add(fib[i]);
                    s -= fib[i];
                }
            }
            out.println(result.size());
            for (long x : result) {
                out.print(x + " ");
            }
            out.println("");
        }

    }

    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());
        }

    }
}