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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>

int maxdiff(int a, int b, int c) {
    int diff[6] = {
        a - b,
        a - c,
        b - a,
        b - c,
        c - a,
        c - b
    };

    int max = -INFINITY;
    for (int i = 0; i < 6; i++) {
        if (diff[i] > max) {
            max = diff[i];
        }
    }
    return max;
}


int main(void) {
    int H, W;
    scanf("%d %d", &H, &W);

    int HW = H * W;
    if (HW % 3 == 0) {
        printf("0\n");
        return 0;
    }

    int a, b, c, diff = INFINITY;
    for (int h = 1; h < H - 1; h++) {
        a = h * W;

        int bw = W / 2;
        b = (H - h) * bw;

        c = (H - h) * (W - bw);

        int tmp = maxdiff(a, b, c);
        if (tmp < diff) {
            printf("a=%d b=%d c=%d\n", a, b, c);
            diff = tmp;
        }

        int bh = H / 2;
        b = bh * W;

        c = (h - bh) * W;

        int tmp2 = maxdiff(a, b, c);
        if (tmp2 < diff) {
            printf("a=%d b=%d c=%d\n", a, b, c);
            diff = tmp2;
        }
    }

    for (int w = 1; w < W - 1; w++) {
        a = H * w;

        int bh = H / 2;
        b = bh * (W - w);

        c = (H - bh) * (W - w);

        int tmp = maxdiff(a, b, c);
        if (tmp < diff) {
            printf("a=%d b=%d c=%d\n", a, b, c);
            diff = tmp;
        }

        int bw = W / 2;
        b = H * bw;

        c = H * (w - bw);

        int tmp2 = maxdiff(a, b, c);
        if (tmp2 < diff) {
            printf("a=%d b=%d c=%d\n", a, b, c);
            diff = tmp2;
        }
    }


    printf("%d\n", diff);

    return 0;
}