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>
#include<math.h>
long int mindis(long int, long int, long int);

int main(void)
{
int h,w,a1,a2,a3,lng,shrt;
unsigned long int s1,s2,s3,d, min;

scanf("%d %d", &h, &w);

if(h%3==0 || w%3==0){
  printf("0\n");
}
else {

shrt = h;
lng = w;

//-----
a1 = lng / 3+ lng%3/2;
a2 = shrt / 2;

s1 = shrt * a1;
s2 = a2 * (lng - a1);
s3 = (shrt - a2) * (lng - a1);
min = mindis(s1,s2,s3);

//-----
a2 = (lng-a1) / 2;
a3 = lng - a1 - a2;
s1 = shrt * a1;
s2 = shrt * a2;
s3 = shrt * a3;

d = mindis(s1,s2,s3);
if(min > d) min=d;

shrt = w;
lng = h;

//-----
a1 = lng / 3+ lng%3/2;
a2 = shrt / 2;

s1 = shrt * a1;
s2 = a2 * (lng - a1);
s3 = (shrt - a2) * (lng - a1);

d = mindis(s1,s2,s3);
if(min > d) min=d;


//-----
a2 = (lng-a1) / 2;
a3 = lng - a1 - a2;
s1 = shrt * a1;
s2 = shrt * a2;
s3 = shrt * a3;

d = mindis(s1,s2,s3);
if(min > d) min=d;

printf("%ld\n", min);
}

return 0;
}

long int mindis(long int s1, long int s2, long int s3){
long int d;
if(s3 > s2) {
  if(s2 > s1) {
    d=s3-s1;
  }else{
    if(s3 > s1){
      d=s3-s2;
    }else{ 
      d=s1-s2;
    }
  }
}else{
  if(s1 > s2){
    d=s1-s3;
  }else{
    if(s1 < s3){
      d=s2 - s1;
    }else{
      d=s2 - s3;
    }
  }
}
return d;
}