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)

# -*- coding:utf-8 -*-
h,w = map(int,input().split())
if w % 3 == 0 or h % 3 == 0:
    print(0)
elif h % 2 == 1 and w % 2 == 0:
    arr = []
    smax = (h // 3 + 1) * w
    smin = (h - (h//3 + 1)) * (w//2)
    arr.append(smax - smin)
    smax = (w//3 + 1) * h
    smin = (w - (w//3 + 1)) * (h//2)
    arr.append(smax - smin)

    
    smax = (h // 3) * w
    smin = (h - (h//3)) * (w//2)
    if smax - smin >= 0:
        arr.append(smax - smin)
    smax = (w//3) * h
    smin = (w - (w//3)) * (h//2)    
    if smax - smin >= 0:
        arr.append(smax - smin)    
    
    smax = (h//3 + 1) * w
    smin = (h//3) * w
    arr.append(smax - smin)
    smax = (w//3 + 1) * h
    smin = (w//3) * h
    arr.append(smax - smin)    
    print(min(arr))
elif h % 2 == 0 and w % 2 == 1:
    arr = []
    smax = (h // 3 + 1) * w
    smin = (h - (h//3 + 1)) * (w//2)
    arr.append(smax - smin)
    smax = (w//3 + 1) * h
    smin = (w - (w//3 + 1)) * (h//2)
    arr.append(smax - smin)

    smax = (h // 3) * w
    smin = (h - (h//3)) * (w//2)
    if smax - smin >= 0:
        arr.append(smax - smin)
    smax = (w//3) * h
    smin = (w - (w//3)) * (h//2)    
    if smax - smin >= 0:
        arr.append(smax - smin)
    
    
    smax = (h//3 + 1) * w
    smin = (h//3) * w
    arr.append(smax - smin)
    smax = (w//3 + 1) * h
    smin = (w//3) * h
    arr.append(smax - smin)    
    print(min(arr))
elif h % 2 == 1 and w % 2 == 1:
    arr = []
    smax = (h // 3 + 1) * w
    smin = (h - (h//3 + 1)) * (w//2)
    arr.append(smax - smin)
    smax = (w//3 + 1) * h
    smin = (w - (w//3 + 1)) * (h//2)
    arr.append(smax - smin)
    
    smax = (h//3 + 1) * w
    smin = (h//3) * w
    arr.append(smax - smin)
    smax = (w//3 + 1) * h
    smin = (w//3) * h
    arr.append(smax - smin)    
    print(min(arr))
    
else:
    arr = []
    smax = (h // 3 + 1) * w
    smin = (h - (h//3 + 1)) * (w//2)
    arr.append(smax - smin)
    smax = (w//3 + 1) * h
    smin = (w - (w//3 + 1)) * (h//2)
    arr.append(smax - smin)
    
    smax = (h // 3) * w
    smin = (h - (h//3)) * (w//2)
    arr.append(abs(smax - smin))
    smax = (w//3) * h
    smin = (w - (w//3)) * (h//2)    
    arr.append(abs(smax - smin))
    
    smax = (h//3 + 1) * w
    smin = (h//3) * w
    arr.append(smax - smin)
    smax = (w//3 + 1) * h
    smin = (w//3) * h
    arr.append(smax - smin)    
    print(min(arr))