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 check_s(tmp1, tmp2, tmp3):
    S_min = 2 ** 50
    S_max = 0
    S_min = min(S_min, tmp1, tmp2, tmp3)
    S_max = max(S_max, tmp1, tmp2, tmp3)
    return S_max - S_min

if __name__ == "__main__":
    H,W = map(int, input().split())
    if (H > W):
        H,W = W,H
    if (H % 3 == 0 or W % 3 == 0):
        print (0)
        exit()

    result = 2 ** 50
    for x in range(1, W + 1):
        H1 = H // 2
        H2 = H - H1

        W1 = x
        W2 = W - W1

        W3 = W2 // 2
        W4 = W2 - W3

        tmp1 = W1 * H
        tmp2 = W3 * H
        tmp3 = W4 * H

        result = min(result, check_s(tmp1, tmp2, tmp3))
        tmp1 = W1 * H
        tmp2 = W2 * H1
        tmp3 = W2 * H2
        result = min(result, check_s(tmp1, tmp2, tmp3))

    for y in range(1,  H+ 1):
        H1 = y
        H2 = H - H1

        H3 = H2 // 2
        H4 = H3 - H2

        W1 = W // 2
        W2 = W - W1


        tmp1 = H1 * W
        tmp2 = H3 * W
        tmp3 = H4 * W

        result = min(result, check_s(tmp1, tmp2, tmp3))
        tmp1 = H1 * W
        tmp2 = H2 * W1
        tmp3 = H2 * W2
        result = min(result, check_s(tmp1, tmp2, tmp3))


    print (result)