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 Sum(a, l, r):
    s = 0
    for i in range(l, r):
        s += a[i]
    return s

def main():
    F = [1]

    s, k = map(int, raw_input().split())

    n = k
    while True:
        n += 1
        if n > k:
            f = Sum(F, max(0, n - k - k), n - k)

        if f > s:
            break
        F.append(f)
    
    F = F[1:]
    F.reverse()

    res = [0]
    for f in F:
        if s == 0:
            break
        if s >= f:
            res.append(f)
            s -= f

    print len(res)
    print " ".join(map(str, res))


if __name__ == "__main__":
    main()