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 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define PI 3.14159265359
#define NIL -1
using namespace std;
const int64_t MOD = 1e9 + 7;

int main() {
	int64_t H, W;
	cin >> H >> W;

	int64_t dif = H * W;
	for (int i = 1; i < H; i++) {
		int64_t a, b, c, x;
		a = i * W;
		//cout << "a:" << a << endl;
		
		if ((H - i) % 2 == 0) {
			b = (H - i) / 2 * W;
			//cout << "b:" << b << endl;
			x = abs(a - b);
			if (x < dif) dif = x;
		}

		b = (H - i) * (W / 2);
		c = (H - i) * (W - (W / 2));
		//cout << "b:" << b << endl;
		x = abs(max(max(a, b), c) - min(min(a, b), c));
		if (x < dif) dif = x;

		//cout << dif << endl;
	}

	for (int i = 1; i < W; i++) {
		int64_t a, b, c, x;
		a = i * H;

		if ((W - i) % 2 == 0) {
			b = (W - i) / 2 * H;
			x = abs(a - b);
			if (x < dif) dif = x;
		}

		b = (W - i) * (H / 2);
		c = (W - i) * (H - (H / 2));
		x = abs(max(max(a, b), c) - min(min(a, b), c));
		if (x < dif) dif = x;
	}

	cout << dif << endl;
}