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:

// @author Sanzhar
import java.awt.Point;
import java.io.*;
import java.util.*;

public class Template {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer st;

    String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(in.readLine());
            } catch (Exception e) {
            }
        }
        return st.nextToken();
    }

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

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    public void run() throws Exception {
        //in = new BufferedReader(new FileReader("input.txt"));
        //out = new PrintWriter(new FileWriter("output.txt"));
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.flush();
        out.close();
        in.close();
    }

    public void solve() throws Exception {
        int s = nextInt();
        int k = nextInt();
        long[] b = new long[90];
        b[0] = 1;
        int i;
        for (i = 1; i < 90; i++) {
            long sum = 0;
            for (int j = i - 1; j >= i - k && j >= 0; j--) {
                sum += b[j];
            }
            b[i] = sum;
            if (b[i] >= s) {
                break;
            }
        }

        int m = 0;
        long[] ans = new long[1000];
        while (s > 0) {
            if (s >= b[i]) {
                s -= b[i];
                ans[m++] = b[i];
            }
            i--;
        }
        ans[m++] = 0;
        out.println(m);
        for (i = 0; i < m; i++) {
            out.print(ans[i] + " ");
        }
        out.println();
    }

    public static void main(String[] args) throws Exception {
        new Template().run();
    }
}