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

public class P225B {
    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(in, out);
	out.close();
    }

    static class Task {
	public void solve(InputReader in, PrintWriter out) {
	    long s = in.nextInt();
	    int k = in.nextInt();
	    List<Long> l = new ArrayList<>();
	    l.add(0L);
	    l.add(1L);
	    long next = 1;
	    int i = 0;
	    while (next <= s) {
		l.add(next);
		if (i < k - 1)
		    next *= 2;
		else
		    next = 2 * next - l.get(i - k + 2);
		i++;
	    }
	    Set<Long> set = new HashSet<>();
	    for (i = l.size() - 1; i >= 0; i--) {
		if (l.get(i) <= s) {
		    set.add(l.get(i));
		    s -= l.get(i);
		}
		if (s == 0)
		    break;
	    }
	    if (set.size() < 2)
		set.add(0L);
	    out.println(set.size());
	    for (long x : set)
		out.print(x + " ");

	}
    }

    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());
	}

	public String nextLine() {
	    try {
		return reader.readLine();
	    } catch (IOException e) {
		throw new RuntimeException(e);
	    }
	}

	public int[] nextIntArray(int n) {
	    int[] arr = new int[n];
	    for (int i = 0; i < n; i++)
		arr[i] = nextInt();
	    return arr;
	}

    }
}