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())
if k >= 32:
    l = [0]
    for i in range(32):
        if s&(1<<i):
            l.append(1<<i)
    print(len(l))
    print(*l)
else:
    l = [0]*(k-1)+[1]
    while l[-1] <= s:
        l.append(sum(l[-k:]))
    x = []
    for i in l[::-1]:
        if i and i <= s:
            s -= i
            x.append(i)
    if len(x) == 1:
        x.append(0)
    print(len(x))
    print(*x)
