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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

int main()
{
    long long h, w;
    scanf("%lld%lld", &h, &w);
    if (h % 3 == 0 || w % 3 == 0)
    {
        printf("0\n");
        return 0;
    }
    long long min{h};
    for (int i = 1; i < h; i++)
    {
        long long min_table[3]{i * w, (h - i) * (w / 2), (h - i) * ((w + 1) / 2)};
        long long tmp_min = *std::max_element(min_table, min_table + 3) - *std::min_element(min_table, min_table + 3);
        min = std::min(min, tmp_min);
    }
    for (int i = 1; i < w; i++)
    {
        long long min_table[3]{i * h, (w - i) * (h / 2), (w - i) * ((h + 1) / 2)};
        long long tmp_min = *std::max_element(min_table, min_table + 3) - *std::min_element(min_table, min_table + 3);
        min = std::min(min, tmp_min);
    }
    printf("%lld\n", min);
    
    return 0;
}