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.InputStreamReader;
import java.util.StringTokenizer;

public class B {
    static long[] a;
    static int n;

    public static void main(String[] args) throws IOException {
        InputReader in = new InputReader();
        long s = in.nextInt();
        int k = in.nextInt();
        a = new long[100];
        a[0] = 0;
        a[1] = 1;
        a[2] = 1;
        // a[k] = 1;
        // a[k + 1] = 1;
        for (int i = 3; i < 100; i++) {
            a[i] = (2 * a[i - 1] - ((i - k - 1) >= 0 ? a[i - k - 1] : 0));
            if (a[i] > 1000000000) {
                n = i + 1;
                break;
            }
        }
        // for (int i = 0; i < n; i++)
        // System.out.println(a[i]);
        boolean[] v = new boolean[n];
        v[0] = true;
        solve(v, s);
        int m = 0;
        for (int i = 0; i < n; i++)
            if (v[i])
                m++;
        System.out.println(m);
        for (int i = 0; i < n; i++)
            if (v[i])
                System.out.print(a[i] + " ");
    }

    static boolean found = false;

    public static void solve(boolean[] v, long cur) {
        if (cur == 0)
            found = true;
        if (found)
            return;
        for (int i = n - 1; i >= 0; i--) {
            if (a[i] <= cur && !v[i]) {
                v[i] = true;
                solve(v, cur - a[i]);
                if (found)
                    return;
                v[i] = false;
            }
        }
    }

    static class InputReader {
        BufferedReader in;
        StringTokenizer st;

        public InputReader() throws IOException {
            in = new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer(in.readLine());
        }

        public String next() throws IOException {
            while (!st.hasMoreElements())
                st = new StringTokenizer(in.readLine());
            return st.nextToken();
        }

        public int nextInt() throws NumberFormatException, IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws NumberFormatException, IOException {
            return Long.parseLong(next());
        }
    }

}