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:

fibarr = []
dp = []
predecessor = []
def gen_list(s, k):
    global fibarr
    
    fibarr = [0, 1, 1]
    idx = 3
    while fibarr[idx - 1] <= s :
        fibarr.append(fibarr[idx-1] * 2 - fibarr[max(idx - k - 1, 0)])
        idx += 1    
    
if __name__ == '__main__': 
    int_s, int_k = map(int, raw_input().split())
    
    gen_list(int_s, int_k)
    int_rem = int_s
    answer = []
    for ii in xrange(len(fibarr)-1, -1, -1) :
        if int_rem == 0 :
            break
        if (fibarr[ii] > int_rem) :
            continue
        else :
            int_rem -= fibarr[ii]
            answer.append(fibarr[ii])
    if len(answer)==1 :
        answer.append(0)
    #print fibarr
    
    print len(answer)
    res = ""
    for item in answer :
        res+=str(item)+" "
    res = res[0:len(res)-1]
    print res
    pass