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())

bona = [1]

cnt = 0

while bona[-1] < n:
    if cnt < k:
        bona.append(2 ** cnt)
    else:
        bona.append(sum(bona[-k:]))
    cnt += 1

ans = []

while n > 0:
    while bona[-1] > n:
        bona.pop()
    ans.append(bona[-1])
    n -= bona[-1]

if len(ans) == 1:
    ans.append(0)

print len(ans)
print ' '.join(map(str, ans))