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: Wrong Answer)

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


def cut(H, W):
    ans = 10**10
    for i in range(1, H):
        S1 = i*W

        h = H-i  # 残りの高さ
        if W % 2 == 0 or h % 2 == 0:
            S2 = S3 = h*W//2
        else:
            W, h = max(W, h), min(W, h)
            S2 = (W+1)//2*h
            S3 = (W-1)//2*h

        ans = min(ans, max(S1, S2, S3)-min(S1, S2, S3))
    return ans


print(min(cut(H, W), cut(W, H)))