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).
#!/usr/bin/env python
# -*- coding: utf-8 -*-
kbs, ans = [0, 1], [0]
s, k = map(int, raw_input().split())
while kbs[-1] < s:
    kbs.append(sum(kbs[0-min(len(kbs),k):]))
while s > 0:
    if kbs[-1] <= s:
        ans.append(kbs.pop())
        s -= ans[-1]
    else:
        kbs.pop()
print len(ans)
print ' '.join(map(str, ans))