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 main(){
	int h, w;
	scanf("%d%d", &h, &w);
	if(h%3 == 0 || w %3 == 0){
		printf("0\n");
	}else{
		int mi = min(w, h);
		for(int i = 1; i <= h/2; ++i){
			int x = i*w, y = (h-i)*(w/2), z = (h-i)*((w+1)/2);
			//cout<<i<<"&&"<<x<<"**"<<y<<"**"<<z<<endl;
			mi = min(mi, max(x,max(y, z))-min(min(x, y), z));
		}
		for(int i = 1; i <= w/2; ++i){
			int x = i*h, y = (w-i)*(h/2), z = (w-i)*((h+1)/2);
			//cout<<i<<"&&%%%"<<x<<"**"<<y<<"**"<<z<<endl;
			mi = min(mi, max(x,max(y, z))-min(min(x, y), z));
		}
		printf("%d\n", mi);
	}
}