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: Accepted)

# -*- coding: utf-8 -*-


# See:
# https://img.atcoder.jp/arc074/editorial.pdf
def calc(h, w):
    ans = float('inf')

    # Key Insight: ABCのC問題の基本は全探索
    # 分割方法は4通り
    # h, wを入れ替えれば実質2通り

    # 長方形Aの面積saを全探索
    for hi in range(1, h):
        sa = hi * w

        # 残りの長方形の扱い
        # 縦に2分割
        wi = w // 2
        sb = (h - hi) * wi
        sc = (h - hi) * (w - wi)
        ans = min(ans, max(sa, sb, sc) - min(sa, sb, sc))

        # 横に2分割
        hj = (h - hi) // 2
        sb = hj * w
        sc = (h - hi - hj) * w
        ans = min(ans, max(sa, sb, sc) - min(sa, sb, sc))

    return ans


def main():
    h, w = map(int, input().split())

    print(min(calc(h, w), calc(w, h)))


if __name__ == '__main__':
    main()