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 genFib(k, n):
    cur = 1
    ind = -k + 2
    ret = [0, 1]
    while cur <= n:
        ret.append(cur)
        cur += cur
        if ind >= 0:
            cur -= ret[ind]
        ind += 1
    return ret

def get(n, cur, last):
    global f, m
    if n == 0:
        cur.append(0)
        print len(cur)
        print ' '.join(map(str, cur))
        exit(0)
    for i in range(last, m):
        x = f[i]
        if x <= n:
            get(n - x, cur + [x], i + 1)

n, k = map(int, raw_input().split())
f = genFib(k, n)[::-1]
m = len(f)
get(n, [], 0)
exit(1)