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 <stdlib.h>
int main(void)
{
  int H, W, i, a, b, c, max, min, re;
  scanf("%d %d", &H, &W);

  re = H*W;
  for(i = 1; i < H-1; i++){
    int h = (H-i)/2;
    a = i * W;
    b = h * W;
    c = (H-i-h) * W;
    max = a;
    if(max < b) max = b;
    if(max < c) max = c;
    min = a;
    if(min > b) min = b; 
    if(min > c) min = c;

    if(re > abs(max-min)) re = abs(max-min);
  }

  for(i = 1; i < W-1; i++){
    int w = (W-i)/2;
    a = i * H;
    b = w * H;
    c = (W-i-w) * H;
    max = a;
    if(max < b) max = b;
    if(max < c) max = c;
    min = a;
    if(min > b) min = b; 
    if(min > c) min = c;
  
    if(re > abs(max-min)) re = abs(max-min);
  }

  for(i = 1; i < H; i++){
    int w = W/2;
    a = W * i;
    b = (H-i) * w;
    c = (H-i) * (W-w);
    max = a;
    if(max < b) max = b;
    if(max < c) max = c;
    min = a;
    if(min > b) min = b; 
    if(min > c) min = c;

    if(re > abs(max-min)) re = abs(max-min);
  }

for(i = 1; i < W; i++){
  int h = H/2;
    a = H * i;
    b = (W-i) * h;
    c = (W-i) * (H-h);
     max = a;
    if(max < b) max = b;
    if(max < c) max = c;
    min = a;
    if(min > b) min = b; 
    if(min > c) min = c;

    if(re > abs(max-min)) re = abs(max-min);
 }

 printf("%d\n", re);
 return 0;
}