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 PyPy3 (2.4.0) (judge verdict: Accepted)

# https://atcoder.jp/contests/arc074/tasks/arc074_a

from math import floor


def solve(H, W):
    # hの全探索
    ans = 10 ** 10
    for h in range(1, H):
        SA = h * W

        # (1) A-B-C 均等割
        dh = floor((H - h) / 2)
        SB = dh * W
        SC = (H - h - dh) * W
        a1 = max(SA, SB, SC) - min(SA, SB, SC)
        ans = min(ans, a1)

        # (2) A-B|C
        w = floor(W / 2)
        SB = (H - h) * w
        SC = (H - h) * (W - w)
        a2 = max(SA, SB, SC) - min(SA, SB, SC)
        ans = min(ans, a2)
    return ans


if __name__ == '__main__':
    h, w = map(int, input().split())
    ans1 = solve(h, w)
    ans2 = solve(w, h)
    print(min(ans1, ans2))