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)

a, b = input().split(" ")
a = int(a)
b = int(b)
if b > a:
    a, b = b, a
case1 = 0
case2 = 0
case3 = 0

if a % 3 == 0:
    case1 = 0
else:
    case1 = b

if b % 3 == 0:
    case2 = 0
else:
    case2 = a

con1 = round(a / 3)
sum1 = con1 * b

con2 = a - con1
sum2 = b // 2 * con2
sum3 = (b - b //2) * con2
case3 = (max(sum3, max(sum2, sum1)) - min(sum3, min(sum2, sum1)))

print(min(case3, min(case1, case2)))