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: Accepted)

#include<stdio.h>
double max(double a, double b)
{
    if (a > b)
        return a;
    else
        return b;
}
double min(double a, double b)
{
    if (a < b)
        return a;
    else
        return b;
}
double abs(double a)
{
    if (a >= 0)
        return a;
    else
        return -a;
}
int main()
{
    long long int h, w;
    scanf("%lld %lld", &h, &w);
    if (h % 3 == 0 || w % 3 == 0)
    {
        printf("0\n");
        return 0;
    }
    long long int i;
    unsigned long long int ans = 2000000000;
    i = h / 3;
    ans = min(ans, min(w*(h + 1 - i) / 2, (h - i)*((w + 1) / 2)) - (i*w));
    i++;
    ans = min(ans, (w*i) - max(w*((h - i) / 2), (h - i)*(w / 2)));
    i = w / 3;
    ans = min(ans, min(h*(w + 1 - i) / 2, (w - i)*((h + 1) / 2)) - (i*h));
    i++;
    ans = min(ans, (h*i) - max(h*((w - i) / 2), (w - i)*(h / 2)));
    printf("%lld\n", ans);
    return 0;
}