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.LinkedList;
import java.util.Scanner;

public class B {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int s = in.nextInt();
        int k = in.nextInt();
        long[] DP = new long[100];
        DP[0] = 1;
        int i;
        for (i = 1; i < 100; i++) {
            for (int j = Math.max(0, i - k); j < i; j++)
                DP[i] += DP[j];
            if (DP[i] > s)
                break;
        }
        i--;
        LinkedList<Long> ans = new LinkedList<Long>();
        for (int j = i; j >= 0; j--) {
            if (DP[j] <= s) {
                ans.add(DP[j]);
                s -= DP[j];
            }
        }
        if (ans.size() < 2)
            ans.add(0l);
        System.out.println(ans.size());
        for (long x : ans)
            System.out.print(x + " ");
        System.out.println();
    }
}