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())
f = [1]
while f[-1] < s:
	x = 0
	for i in range(max(0, len(f)-k), len(f)):
		x += f[i]
	f.append(x)
result = [0]
pos = len(f)-1
while s != 0:
	while f[pos] > s:
		pos -= 1
	result.append(f[pos])
	s -= f[pos]
print(len(result))
print(' '.join(map(str, result)))
