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 = list(map(int, input().split()))
ans = float("inf")
if H % 3 == 0 or W % 3 == 0:
    ans = 0
else:
    for i in range(1, W):
        a = H * i
        b = (W - i) * (H // 2)
        c = H * W - a - b
        S_min = min(a, min(b, c))
        S_max = max(a, max(b, c))
        ans = min(ans, S_max - S_min)
    for i in range(1, H):
        a = W * i
        b = (H - i) * (W // 2)
        c = H * W - a - b
        S_min = min(a, min(b, c))
        S_max = max(a, max(b, c))
        ans = min(ans, S_max - S_min)

print(ans)