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)

import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]

def main():
    # ||,|-,--,-|全部試す
    h, w = MI()
    a = []
    l1 = w // 3
    for w0 in [l1, l1 + 1]:
        p1 = w0 * h
        w12 = w - w0
        l2 = w12 // 3
        for w1 in [l2, l2 + 1]:
            p2 = w1 * h
            a.append(max(p1, p2, h * w - p1 - p2) - min(p1, p2, h * w - p1 - p2))
        u = h // 2
        for h1 in [u, u + 1]:
            p2 = w12 * h1
            a.append(max(p1, p2, h * w - p1 - p2) - min(p1, p2, h * w - p1 - p2))
    u1 = h // 3
    for h0 in [u1, u1 + 1]:
        p1 = h0 * w
        h12 = h - h0
        u2 = h12 // 2
        for h1 in [u2, u2 + 1]:
            p2 = h1 * w
            a.append(max(p1, p2, h * w - p1 - p2) - min(p1, p2, h * w - p1 - p2))
        l = w // 2
        for w1 in [l, l + 1]:
            p2 = h12 * w1
            a.append(max(p1, p2, h * w - p1 - p2) - min(p1, p2, h * w - p1 - p2))
    print(min(a))

main()