Numbers *k*-bonacci (*k* is integer, *k* &gt; 1) are a generalization of Fibonacci numbers and are determined as follows:
 -  *F*(*k*, *n*) = 0, for integer *n*, 1 ≤ *n* &lt; *k*; -  *F*(*k*, *k*) = 1; -  *F*(*k*, *n*) = *F*(*k*, *n* - 1) + *F*(*k*, *n* - 2) + ... + *F*(*k*, *n* - *k*), for integer *n*, *n* &gt; *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.
The first line contains two integers *s* and *k* (1 ≤ *s*, *k* ≤ 10<sup class="upper-index">9</sup>; *k* &gt; 1).
[s, k] = [int(x) for x in input().split()]
if s == 1:
    print(2)
    print(1,0)
    exit()
numbers = [1]
numbers.append(1)

last = 1
index = 1
while last < s:
    l_index = index-k
    if l_index >= 0:
        last = last * 2 - numbers[l_index]
    else:
        last *= 2
    # print(last, l_index)
    if last != s:
        numbers.append(last)
    index += 1

numbers.reverse()

# for s in range(0, 100000):
output = []
for i in numbers:
    if i <= s:
        s -= i
        output.append(i)

print(len(output))
print(" ".join([str(x) for x in output]))




