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>

int main(void)
{
    int h,w;
    scanf("%d %d",&h,&w);
    
    if(h % 3 == 0|| w % 3 == 0){
        printf("0\n");
    }
    else if(h == w){
        if(h % 2 == 0)printf("%d\n",h/2);
        else printf("%d\n",h-1);
    }
    else if(w % 2 == 0){
        if(h % 2 == 1 && h < w/2) printf("%d\n",h);
        else printf("%d\n",w/2);
    }
    else if(w % 2 == 1){
        if(h % 2 == 0 && h/2 < w) printf("%d\n",h/2);
        else printf("%d\n",w);
    }
    return 0;
}