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: Accepted)

#include <bits/stdc++.h>
using namespace std;

int solve(int h, int w) {
    int a[4];
    int s[3];
    int dh = (h + 1) / 3;
    s[0] = dh * w;
    s[1] = ((h - dh) / 2) * w;
    s[2] = (h - dh - (h - dh) / 2) * w;
    sort(s, s + 3);
    a[0] = s[2] - s[0];

    s[0] = dh * w;
    s[1] = (w / 2) * (h - dh);
    s[2] = (w - w / 2) * (h - dh);
    sort(s, s + 3);
    a[1] = s[2] - s[0];

    int dw = (w + 1) / 3;
    s[0] = h * dw;
    s[1] = ((w - dw) / 2) * h;
    s[2] = (w - dw - (w - dw) / 2) * h;
    sort(s, s + 3);
    a[2] = s[2] - s[0];

    s[0] = h * dw;
    s[1] = (h / 2) * (w - dw);
    s[2] = (h - h / 2) * (w - dw);
    sort(s, s + 3);
    a[3] = s[2] - s[0];
    return a[min_element(a, a + 4) - a];
}

int main() {
    int h, w;
    cin >> h >> w;
    cout << solve(h, w) << endl;
    return 0;
}