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: Runtime Error)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import array
from bisect import *
from collections import *
import fractions
import heapq 
from itertools import *
import math
import re
import string

def max_minus_min(areas):
    # print("areas", areas)
    return max(areas) - min(areas)

def solve2(h, w):
    area1 = h * (w // 2)
    area2 = h * w - area1
    return area1, area2

def solve(h, w):
    w_div_3 = w // 3;
    ans = 1e9
    for w2 in range(w_div_3, w_div_3 + 2):
        area1 = w2 * h
        ans = min(ans, max_minus_min([area1, *solve2(h, w - w2)]))
        ans = min(ans, max_minus_min([area1, *solve2(w - w2, h)]))
    return ans

H, W = map(int, input().split())
print(min(solve(H,W), solve(W,H)))