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>

long ChocolateBar(long h, long w){
  long diff=h*w;

  for(long i=1;i<h;i++){
	long s1 = i * w;
    long s2 = ((h-i+1)/2) * w;
	long s3 = ((h-i)/2) * w;
	long d1 = s1 < s2 ? s2 - s1: s1 - s2;
	long d2 = s1 < s3 ? s3 - s1: s1 - s3;
	long d = d1 < d2 ? d2 : d1;
	//printf("1 %ld %ld %ld\n", s1, s2, s3);
	if(d < diff){
	  diff = d;
	}
	
	s2 = (h-i)*((w+1)/2);
	s3 = (h-i)*(w/2);
	d1 = s1 < s2 ? s2 - s1: s1 - s2;
	d2 = s1 < s3 ? s3 - s1: s1 - s3;
	d = d1 < d2 ? d2 : d1;
	//printf("2 %ld %ld %ld\n", s1, s2, s3);
	if(d < diff){
	  diff = d;
	}
  }

  for(long i=1;i<w;i++){
	long s1 = i * h;
    long s2 = ((w-i+1)/2) * h;
    long s3 = ((w-i)/2) * h;
	long d1 = s1 < s2 ? s2 - s1: s1 - s2;
	long d2 = s1 < s3 ? s3 - s1: s1 - s3;
	long d = d1 < d2 ? d2 : d1;
	//printf("3 %ld %ld %ld\n", s1, s2, s3);
	if(d < diff){
	  diff = d;
	}
	
	s2 = (w-i)*((h+1)/2);
	s3 = (w-i)*(h/2);
	d1 = s1 < s2 ? s2 - s1: s1 - s2;
	d2 = s1 < s3 ? s3 - s1: s1 - s3;
	d = d1 < d2 ? d2 : d1;
	//printf("4 %ld %ld %ld\n", s1, s2, s3);
	if(d < diff){
	  diff = d;
	}
  }
  return diff;
}

int main(int argc, char *argv[]){
  long h, w;
  scanf("%ld %ld", &h, &w);
  printf("%ld", ChocolateBar(h, w));

  return 0;
}