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 PYTHON):

Solution:
n,k=map(int,raw_input().split())
lst=[0,1]
s=1
k=min(k,30)
for i in range(2,k):
  lst.append(s)
  s=s+lst[-1]
for i in range(0,70):
  s=0
  #print i,
  for j in range(i,i+k):
    s=s+lst[j]
    #print s,lst[j],j
  lst.append(s)
ans=[]
#print lst
lc=0
for i in range(len(lst)-1,-1,-1):
  if n>0 and  lst[i]<=n:
    if lst[i] not in ans:
      ans.append(lst[i])
      n=n-lst[i]
      lc=lc+1
if 0 not in ans:
  ans.append(0)
print len(ans)
for i in ans:
  print i,
print