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 bisect 
s,k=list(map(int,input().split()))
f=[0]*45
for i in range(45):
    if i==0 or i==1:
        f[i]=1
    elif i<k:
        f[i]=sum(f[:i])
    else:
        f[i]=sum([f[i-j] for j in range(1,k+1)])
ans=[0]
while s>0:
    i=bisect.bisect_right(f,s)
    ans.append(f[i-1])
    s=s-f[i-1]
print(len(ans))
for i in range(len(ans)):
    print(ans[i],end=' ')