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)

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

if H * W % 3 == 0:
    print(0)
    exit()

S = H * W
a = (S // 3 // H) - 10
b = (S // 3 // W) - 10

ans1 = float('inf')
ans2 = float('inf')
for i in range(a, a + 30):
    if i <= 0 or i >= W:
        continue
    x = i * H
    y = (W - i) * (H//2)
    z = S - x - y
    ans1 = min(ans1, max(x, y, z) - min(x, y, z))

for i in range(b, b + 30):
    if i <= 0 or i >= H:
        continue
    x = i * W
    y = (H - i) * (W//2)
    z = S - x - y
    ans2 = min(ans2, max(x, y, z) - min(x, y, z))
print(min(ans1, ans2, H, W))