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:
import sys
input=sys.stdin.readline
s,k=map(int,input().split())
ans=[]
if k>=60:
  f=[0,1]
  x=1
  for i in range(60):
    f.append(x)
    x+=x
  for i in range(60)[::-1]:
    if s>=f[i]:
      ans.append(f[i])
      s-=f[i]
      if s==0:
        break
else:
  f=[0]*(k-1)+[1]
  x=1
  for i in range(60):
    f.append(x)
    y=x-f[i]
    x+=y
  ans=[]
  for i in range(60)[::-1]:
    if s>=f[i]:
      ans.append(f[i])
      s-=f[i]
      if s==0:
        break
ans.append(0)
print(len(ans))
print(*ans)