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 PYTHON):

Solution:
import sys

def k_fib(k, upper_bound):
    if upper_bound < 2:
        return upper_bound
    f = [1]
    while len(f) < k and f[-1] * 2 <= upper_bound:
        f.append(f[-1] * 2)
    while len(f) == k and sum(f) <= upper_bound:
        f.append(sum(f))
        f.remove(f[0])
    return f[-1]

def main():
    s, k = map(lambda x: int(x), sys.stdin.readline().split())
    a = []
    while s > 0:
        f = k_fib(k, s)
        a.append(f)
        s -= f
    if len(a) == 1:
        a.append(0)
    print len(a)
    print ' '.join(map(lambda x: str(x), a))

if __name__ == '__main__':
    main()