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:
l = [0,1]
s,k = map(int,raw_input().split())
while 1:
    t = sum(l if len(l) < k else l[-1:-1-k:-1])
    if t > s: break
    l.append(t)
r = []
for i in xrange(len(l)-1,-1,-1):
    if s == 0:
        if len(r) < 2: r.append(0)
        break
    elif s >= l[i] and l[i] not in r:
        r.append(l[i])
        s -= l[i]
print len(r)
print ' '.join(map(str,r))