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())
f=[0]
f.append(1)
while(True):
    cur=sum(f[-k:])
    if cur>s:
        break
    f.append(cur)
f=list(set(f))
f.sort()
ans=[]
i=len(f)-1
while(s and i>0):
    if f[i]<=s:
        s-=f[i]
        ans.append(f[i])
    i-=1
print(len(ans)+1)
print(*(ans+[0]))
