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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>

using namespace std;

int chocolate(int x,int y){
	

	if (x%3==0 || y%3==0){

		return (0);
	
	}else{
		
		int x_max, y_max, x_min, y_min;
				
		if(x%3==1){
			x_max = (2*x+1)/3;
			y_max = (y/2 + y%2);
			if (y%2==0){
				y_min = y;
				x_min =  x - x_max;
			}else{
				y_min = y/2;
				x_min =  x_max;
			}
		}else{
			x_max = (x+1)/3;
			x_min = x - x_max;
			y_max = y;
			y_min = (y/2);
		}
		
		
		
		return (x_max*y_max - x_min*y_min);
		
	}
	
	
}


int main()
{

	int h,w;
	cin >> h >> w;

	int ans;
	
	if (h>=w){
		ans = chocolate(h,w);
	}else{
		ans = chocolate(w,h);
	}
	
	cout << ans << "\n";
	
}