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:
def readInt():
    return tuple([int(x) for x in raw_input().split()])

s, k = readInt()
if k >= 40:
    fib = [2**i for i in xrange(40)]
else:
    fib = [0] * (k - 1) + [1]
    while fib[-1] < s:
        fib.append(sum(fib[-k:]))
ans = [0]
while s > 0:
    if fib[-1] <= s:
        ans.append(fib[-1])
        s -= fib[-1]
    fib.pop()
print len(ans)
print " ".join([str(x) for x in ans])