Problem: Numbers k-bonacci (k is integer, k > 1) are a generalization of Fibonacci numbers and are determined as follows:

  * F(k, n) = 0, for integer n, 1 ≤ n < k; 
  * F(k, k) = 1; 
  * F(k, n) = F(k, n - 1) + F(k, n - 2) + ... + F(k, n - k), for integer n, n > 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. 

Input

The first line contains two integers s and k (1 ≤ s, k ≤ 109; k > 1).

Output

In the first line print an integer m (m ≥ 2) that shows how many numbers are in the found representation. In the second line print m distinct integers a1, a2, ..., am. Each printed integer should be a k-bonacci number. The sum of printed integers must equal s.

It is guaranteed that the answer exists. If there are several possible answers, print any of them.

Examples

Input

5 2


Output

3
0 2 3


Input

21 5


Output

3
4 1 16

Solution (in PYTHON3):

Solution:
s,k=list(map(int,input().split()))
a=[1]
i=0
while s>a[-1]:
    if i==0:
        a.append(1)
    else:
        a.append(2*a[-1]-int(a[-k-1] if i>=k else 0))
    i+=1
b=[]
s0=s
while s>0:
    l,r=-1,i+1
    while r-l>1:
        m=(l+r)//2
        if a[m]>=s:
            r=m
        else:
            l=m
    r=min(i,r)
    while a[r]>s:
        r-=1
    s-=a[r]
    b.append(a[r])
if len(b)==1:
    b.append(0)
print(len(b))
print(*b)