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.List;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.FileReader;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.ArrayList;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.File;
import java.io.Writer;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author unnamed
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskB {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        long s = in.nextInt(), k = in.nextInt();
        long[] table = new long[50];
        table[0] = 1;
        table[1] = 1;
        boolean enough = false;
        for (int i = 2; !enough & i < 50; ++i) {
            int j = 1;
            int f = 0;
            while (j <= k & i - j >= 0 & f <= s) {
                f += table[i - j];
                if (f > s)
                    enough = true;
                ++j;
            }
            if (!enough) table[i] = f;
        }
        int len = 0;
        while (table[len] != 0 & len < 50)
            ++len;
        long[] ans = new long[len];
        for (int i = 0; i < len; ++i)
            ans[i] = table[i];
        ans[0] = 0;
        List<Long> res = new ArrayList<Long>();
        while (s > 0) {
            int ke = Arrays.binarySearch(ans, s);
            if (ke < 0)
                ke = -ke - 2;
            res.add(ans[ke]);
            s -= ans[ke];
        }
        if (res.size() == 1)
            res.add(0L);
        out.println(res.size());
        for (long i : res)
            out.print(i + " ");
    }
}

class InputReader {
    BufferedReader br;
    StringTokenizer st;

    public InputReader(File f) {
        try {
            br = new BufferedReader(new FileReader(f));
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    public InputReader(InputStream f) {
        br = new BufferedReader(new InputStreamReader(f));
    }

    public String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

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

    }

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void println(Object... objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }
}