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 (7.3.0) (judge verdict: Wrong Answer)

H,W = map(int,input().split())
Min = float('inf')
if H >= 3:
    Min = min(Min, (H%3)*W)
if W>=3:
    Min = min(Min, (W%3)*H)

for h in range(1,H):
    cake1 = h*W
    cake2 = (H-h)*(W//2)
    cake3 = (H-h)*(-(-W//2))
    big = max(cake1,cake2,cake3)
    small = min(cake1,cake2,cake3)
    Min = min(Min,big-small)


for w in range(1,W):
    cake1 = w*H
    cake2 = (W-w)*(H//2)
    cake3 = (W-w)*(-(-H//2))
    big = max(cake1,cake2,cake3)
    small = min(cake1,cake2,cake3)
    Min = min(Min,big-small)

print(Min)