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 = map(int, input().split())
freq = [1]
while freq[-1] < s:
	x = 0
	for i in range(max(0, len(freq)-k), len(freq)):
		x += freq[i]
	freq.append(x)
res = [0]
idx = len(freq) - 1
while s != 0:
	while freq[idx] > s:
		idx -= 1
	res.append(freq[idx])
	s -= freq[idx]
print(len(res))
print(*res)
