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 (3.4.3) (judge verdict: Runtime Error)

#!/usr/bin/env python3
import sys


def f(H, W):
    mh = H // 2
    mw = W // 2
    return (mh*W, (H-mh)*W), (H*mw, H*(W-mw))

def solve_iter(H: int, W: int):
    for h in range(1, H):
        for s in ((h*W,*s) for s in f(H-h, W)):
            yield max(s) - min(s)
    for w in range(1, W):
        for s in ((H*w,*s) for s in f(H, W-w)):
            yield max(s) - min(s)

def solve(H: int, W: int):
    return min(solve_iter(H, W))


# Generated by 1.1.7.1 https://github.com/kyuridenamida/atcoder-tools
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    H = int(next(tokens))  # type: int
    W = int(next(tokens))  # type: int
    print(solve(H, W))

def test():
    import doctest
    doctest.testmod()

if __name__ == '__main__':
    #test()
    main()