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).
from sys import stdin
input = stdin.readline

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

ans = []
t = [0]*k
t[-1] = 1
for i in range(k+1, 40):
    x = sum(t[len(t)-k:])
    t.append(x)
    if t[-1] >= s:
        i = len(t)-1
        while s:
            if t[i] == 1:
                ans += [1]*s
                print(len(ans)); print(*ans); quit()
            else:
                if t[i] < s:
                    s -= t[i]
                    ans.append(t[i])
                if s == 0:
                    print(len(ans)); print(*ans); quit()
            i -= 1
    