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.io.PrintWriter;

public class ProblemB {
    
    public static void main(String[] args) throws IOException {
        BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
        String[] line = s.readLine().split(" ");
        long n = Long.valueOf(line[0]);
        int k = Integer.valueOf(line[1]);
        if (k >= 32) {
            int cnt = Long.bitCount(n) + 1;
            StringBuffer ans = new StringBuffer();
            ans.append(cnt).append(" ").append(0).append(" ");
            for (int i = 0 ; i < 32 ; i++) {
                if ((n & (1<<i)) >= 1) {
                    ans.append(1<<i).append(" ");
                }
            }
            System.out.println(ans.substring(0, ans.length()-1));
            return;
        } 
        
        long[] table = new long[1000000];
        table[k] = 1;
        
        int now = -1;
        for (int i = k+1 ; i < 1000000 ; i++) {
            for (int j = i-1 ; j >= i-k ; j--) {
                table[i] += table[j];
            }
            if (table[i] >= n) {
                now = i;
                break;
            }
        }
        
        StringBuffer ans = new StringBuffer();
        ans.append(0);
        int cnt = 1;
        while (n >= 1) {
            if (table[now] <= n) {
                ans.append(" ").append(table[now]);
                cnt++;
                n -= table[now];
            }
            now--;
        }
        System.out.println(cnt + " " + ans.toString());
    }
}