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=list(map(int,input().split(' ')))
a=[0,1,1]
while a[-1]<s:
    if len(a)<k:
        a.append(sum(a))
    else:
        t=0
        for i in range(k):
            t+=a[-i-1]
        a.append(t)
if s==a[-1]:
    print(2)
    print(0,a[-1])
else:
    use=[]
    for i in range(len(a)):
        if s>=a[-i-1]:
            s-=a[-i-1]
            use.append(a[-i-1])
    print(len(use))
    for i in use:
        print(i,end=' ')