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: Wrong Answer)

H, W = list(map(int, input().split()))

# 3の倍数の場合
if H * W % 3 == 0:
    print(0)
else:

    # 縦長にする
    H, W = max(H, W), min(H, W)

    # |-パターン
    BCh = 0
    Bw, Cw = W // 2, W // 2
    if W % 2 == 1:
        Bw += 1

    def get_abs(BCh):
        """
        最大最小の面積の差
        """
        S_B = BCh * Bw
        S_C = BCh * Cw
        S_A = W * (H - BCh)  # max
        # print(S_A)
        return abs(max([S_A, S_B, S_C]) - min([S_A, S_B, S_C]))

    # print(Bw)
    err = get_abs(BCh)
    # print(err)
    for h in range(1, H):
        new_err = get_abs(h)
        if new_err < err:
            err = new_err
            # print(h, err)
        else:
            break

        # else:
        #     break

    # ||パターン
    Hmin = H // 3
    Hmax = H // 3 + H % 3
    err2 = (Hmax - Hmin) * W
    if err2 < err:
        err = err2

    print(err)