Problem:
Score : 400 points

Problem Statement

There is a bar of chocolate with a height of H blocks and a width of W blocks.
Snuke is dividing this bar into exactly three pieces.
He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.

Snuke is trying to divide the bar as evenly as possible.
More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.
Find the minimum possible value of S_{max} - S_{min}.

Constraints

2 ≤ H, W ≤ 10^5

Input

Input is given from Standard Input in the following format:

H W

Output

Print the minimum possible value of S_{max} - S_{min}.

Sample Input 1

3 5

Sample Output 1

0

In the division below, S_{max} - S_{min} = 5 - 5 = 0.

Sample Input 2

4 5

Sample Output 2

2

In the division below, S_{max} - S_{min} = 8 - 6 = 2.

Sample Input 3

5 5

Sample Output 3

4

In the division below, S_{max} - S_{min} = 10 - 6 = 4.

Sample Input 4

100000 2

Sample Output 4

1

Sample Input 5

100000 100000

Sample Output 5

50000

Solution in Python (3.8.2) (judge verdict: Accepted)

def calc(h, w):
  ans = (h+1)*(w+1)
  cut_1 = h//2
  cut_2 = h//2 + (h%2 == 1)
  for i in range(1, w):
    s1 = [h*i, cut_1*(w-i), cut_2*(w-i)]
    s2 = [h*i, h*((w-i)//2), h*((w-i)//2+ ((w-i)%2 == 1))]
    ans = min([ans, max(s1)-min(s1), max(s2)-min(s2)])
  return ans
def main():
  a, b = map(int,  input().split())
  print(min([calc(a,  b), calc(b, a)]))
  
if __name__ == "__main__":
  main()