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] = [int(x) for x in input().split()]

numbers = [1]
numbers.append(1)

last = 1
index = 1
while last <= s:
    l_index = index-k
    if l_index >= 0:
        last = last * 2 - numbers[l_index]
    else:
        last *= 2
    # print(last, l_index)
    if last <= s:
        numbers.append(last)
    index += 1


numbers.reverse()
numbers.append(0)

# for s in range(0, 100000):
output = []
for i in numbers:
    if i <= s:
        s -= i
        output.append(i)

print(len(output))
print(" ".join([str(x) for x in output]))