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
# Your code here!
h,w = [int(i) for i in input().split()]

def once(h,w):
    res = 10**9
    if h > 1:
        a,b = h//2*w, (h-h//2)*w
        res = abs(a-b)
    if w > 1:
        c,d = w//2*h, (w-w//2)*h
        if abs(c-d) < res:
            a,b = c,d
    return a,b    


def hsaki(h,w):
    res = 10**9
    for i in range(1,h):
        p1 = i*w
        p2,p3 = once(h-i,w)
        a = max(p1,p2,p3) - min(p1,p2,p3) 
        res = min(res, a)
#        print(p1,p2,p3)
    return res

#print(hsaki(h,w), hsaki(w,h))

ans = min(hsaki(h,w), hsaki(w,h))
print(ans)