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:

myin = raw_input()
myin = myin.split()

mysum = int(myin[0])
myk = int(myin[1])

kbon = [0]
kbon.append(1)

while kbon[len(kbon) - 1] < mysum:
    if len(kbon) < myk:
        kbon.append(sum(kbon))
    else:
        temp = 0
        for i in range(myk):
            temp += kbon[len(kbon) - 1 - i]
        kbon.append(temp)

myout = []

mysumtemp = mysum
count = 0

for i in range(len(kbon) - 1, -1, -1):
    if kbon[i] == 0:
        count += 1
        if count == 2:
            break
    if kbon[i] <= mysumtemp:
        myout.append(kbon[i])
        mysumtemp -= kbon[i]


print len(myout)
outtemp = ''
for i in myout:
    outtemp += str(i) + ' '

outtemp = outtemp[:len(outtemp) - 1]
print outtemp