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]*k
a[k-1]=1
i=0
while s>a[-1]:
    if i==0:
        a.append(1)
    else:
        a.append(2*a[-1]-a[-k-1])
    i+=1
b=[]
while s>0:
    l,r=k-1,k+i+1
    while r-l>1:
        m=(l+r)//2
        if a[m]>=s:
            r=m
        else:
            l=m
    while a[r]>s:
        r-=1
    s-=a[r]
    b.append(a[r])
print(len(b))
print(*b)