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.IOException;
import java.io.OutputStreamWriter;
import java.math.BigDecimal;
import java.io.BufferedWriter;
import java.util.Locale;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigInteger;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Jacob Jiang
 */
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.nextLong();
        if (s == 1) {
            out.println(2);
            out.println("0 1");
            return;
        }
        long k = in.nextLong();
        List<Long> sequence = new ArrayList<Long>();
        sequence.add(1L);
        while (sequence.get(sequence.size() - 1) < s) {
            long item = 0;
            for (int i = (int) Math.max(sequence.size() - k, 0); i < sequence.size(); i++) {
                item += sequence.get(i);
            }
            sequence.add(item);
        }
        List<Long> answer = new ArrayList<Long>();
        for (int i = sequence.size() - 1; i >= 0; i--) {
            long item = sequence.get(i);
            if (s >= item) {
                s -= item;
                answer.add(item);
            }
        }
        if (answer.size() <= 1)
            answer.add(0L);
        Collections.shuffle(answer);
        out.println(answer.size());
        out.printLine(answer.toArray());
    }
}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1 << 16];
    private int curChar;
    private int numChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public static boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public long nextLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c & 15;
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    }

class OutputWriter {
    private PrintWriter writer;

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

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

    public void println(int x) {
        writer.println(x);
    }

    public void print(Object obj) {
        writer.print(obj);
    }

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

    public void println(String x) {
        writer.println(x);
    }

    public void print(char c) {
        writer.print(c);
    }

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

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

    public void printLine(Object... items) {
        printItems(items);
        println();
    }

}