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())
a=[]
series=[]
n=0
while sum(series)<=s:
    if n+1<k:
        series.append(0)
    elif n+1==k:
        series.append(1)
    else:
        series.append(sum(series[n-k:n]))
    n+=1
while(s!=0):
    series.sort(reverse=True)
    a.append(series[0])
    s-=series.pop(0)
    while sum(series)>=s and s!=0: x=series.pop(0)
    series.append(x);series.sort()
    
print(len(a))
print(*a)
