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.*;
import java.lang.*;
import java.math.*;

public class Main {

	public static void main (String[] args) {
        try {
            InputStream         inputstream = System.in;
            InputReader         cin = new InputReader(inputstream);
            PrintWriter         cout = new PrintWriter(System.out, true);
            // FileReader          fin = new FileReader("data.in");
            // InputReader         cin = new InputReader(fin);
            // PrintWriter         cout = new PrintWriter("data.out");
            Task                solver = new Task();
            solver.solve(cin, cout);
            cout.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
	}

}    

class Task {

    public void solve (InputReader cin, PrintWriter cout) {
        long        s, k;
        long        os;
        long[]      fib = new long[61];
        long[]      ans = new long[61];
        int         pt = 0;        
        s = cin.nextLong();
        k = cin.nextLong();
        os = s;
        Arrays.fill(ans, 0);
        fib[0] = 1;
        for (int i = 1; i < 61; ++i) {
            for (int j = i - 1; j >= 0 && j >= i - k; --j) {
                fib[i] += fib[j];
            }
        }
        for (int i = 60; i > 0; --i) {
            if (fib[i] == s) {
                ans[pt] = fib[i];
                pt++;
                ans[pt] = 0;
                pt++;
                break;
            }
            if (fib[i] < s) {
                s -= fib[i];
                ans[pt] = fib[i];
                pt++;
            }
        }
        cout.println(pt);
        for (int i = 0; i < pt; ++i) {
            if (i != 0) {
                cout.print(" ");
            }
            cout.print(ans[i]);
        }
        cout.println();
    }

}

class InputReader {
    private BufferedReader      reader;
    private StringTokenizer     tokenizer;

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

    public InputReader (FileReader fin) {
        reader = new BufferedReader(fin);
        tokenizer = null;
    }

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

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

    public double nextDouble() {
        return Double.parseDouble(nextToken());
    }

    public char nextChar() {
        return nextToken().charAt(0);
    }

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