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)

def div2(h, w):
    if h % 2 == 0 or w % 2 == 0:
        return [h * w // 2] * 2
    if h > w:
        h, w = w, h
    return [h * (w - 1) // 2, h * (w + 1) // 2]


def solve(h, w):
    if h % 3 == 0 or w % 3 == 0:
        return 0
    d1 = w // 3
    areas1 = sorted([h * d1] + div2(h, w - d1))
    ans1 = areas1[-1] - areas1[0]
    d1 += 1
    areas2 = sorted([h * d1] + div2(h, w - d1))
    ans2 = areas2[-1] - areas2[0]

    d2 = h // 3
    areas3 = sorted([d2 * w] + div2(h - d2, w))
    ans3 = areas3[-1] - areas3[0]
    d2 += 1
    areas4 = sorted([d2 * w] + div2(h - d2, w))
    ans4 = areas4[-1] - areas4[0]

    return min(ans1, ans2, ans3, ans4)


print(solve(*map(int, input().split())))