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>
long int returnGAP(long int w,long int h){
	long int ww, hh,s1,s2,nowmin;
	if(w%3==0)return 0;
	ww =w/3;//以下Bなら
	hh = h/2;
	nowmin = (h-hh)*(w-ww) -(h*ww);
	s2 =(w-ww);
	if(s2>nowmin)nowmin=s2;
	ww++;
	s1 = (h*ww) -(hh*(w-ww));
	if(s1<nowmin)nowmin=s1;
	s2 =(w-ww);
	if(s2>s1 && s1==nowmin)nowmin=s2;
	return nowmin;
}

int main(void){
	long int k,l,x,y;
	scanf("%d %d",&k,&l);
	x =returnGAP(k,l);
	y =returnGAP(l,k);
	printf("%d",x>y? y:x);
	return 0;
}