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).
input1 = list(map(int,input().split()))
s = input1[0]
k = input1[1]

k_bonacci = list(map(int,['0']*(k-1)))
k_bonacci.append(1)


i = k
while True:
    if sum(k_bonacci[i-k:i]) >= s:
        break
    k_bonacci.append(sum(k_bonacci[i-k:i]))
    
    i += 1

k_bonacci = k_bonacci[k-2::]
#print(k_bonacci)
output = []
for i in k_bonacci[::-1]:
    if i <= s:
        s -= i
        output.append(i)
    

print(len(output))
print(' '.join(list(map(str,output))))

