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).
import itertools


s, k = [int(x) for x in input().split()]


class vault:
    v = dict()

    def __getitem__(self, item):
        if vault.v.get(item) is None:
            vault.v[item] = get_next(k, item)
        return vault.v[item]

def get_next(k, n):
    # get next kabonachi num
    if n <= k:
        return 0 if n < k else 1
    result = 0
    for x in range(1, k+1):
        result += va[n-x]
        #result += get_next(k, n-x)
    return result

va = vault()
kNums = {get_next(k, x) for x in range(k, s+1) if get_next(k, x-1) <= s}
for x in range(2, 10000):
    for p in itertools.permutations(kNums, x):
        ss = 0
        for i in range (x):
            ss+=p[i]
        if ss == s:
            print(x)
            string = str(p[0])
            for i in range(1, x):
                string+=(' '+str(p[i]))
            print(string)
            exit()