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)

def rren(): return list(map(int, input().split()))


H, W = rren()
if(H % 3 == 0 or W % 3 == 0):
    print(0)
else:
    lis = []
    ans = 114514810
    for i in range(H-1):
        a = H - i
        b = i
        c = W // 2
        lis = [W*a, b*c, (W-c)*b]
        ans = min(ans, max(lis) - min(lis))
        lis.clear()
    for i in range(W-1):
        a = W - i
        b = i
        c = H // 2
        lis = [H*a, b*c, (H-c)*b]
        ans = min(ans, max(lis) - min(lis))
        lis.clear()
    for i in range(W//3, W//2):
        ans = min(ans, abs(i - ((W-i)*2))*H)
    for i in range(H//3, H//2):
        ans = min(ans, abs(i - ((H-i)*2))*W)
    print(ans)