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: Accepted)

# coding: utf-8

import math
import sys


def split_3(h, w):
    cand = []
    cand.extend([(h // 3 + i, w, h - (h // 3 + i), w) for i in range(3)])
    cand.extend([(h, w // 3 + i, h, w - (w // 3 + i)) for i in range(3)])
    return cand


def split_2(h, w):
    cand = []
    cand.extend([((h // 2 + i) * w, (h - (h // 2 + i)) * w) for i in range(2)])
    cand.extend([(h * (w // 2 + i), h * (w - (w // 2 + i))) for i in range(2)])
    return cand


def main():
    h, w = map(int, input().split())
    if h % 3 == 0 or w % 3 == 0:
        return 0

    cand = split_3(h, w)
    score = float("inf")
    for h1, w1, h2, w2 in cand:
        r1 = h1 * w1
        for r2, r3 in split_2(h2, w2):
            score = min(score, max(r1, r2, r3) - min(r1, r2, r3))
    return score


if __name__ == "__main__":
    print(main())