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>
int maxmin(int a, int b, int c){
	int max = a;
	int min = a;
	if(b > max){
		max = b;
	}else if(b < min){
		min = b;
	}
	if(c > max){
		max = c;
	}else if(c < min){
		min = c;
	}
	return max - min;
}

int T(int H, int W){
	int case1, case2, upperHeight, leftWidth;
	upperHeight = H / 3;
	leftWidth = W / 2;
	int S1 = upperHeight * W;
	int S2 = (H - upperHeight) * leftWidth;
	int S3 = (H - upperHeight) * (W - leftWidth);
	case1 = maxmin(S1, S2, S3);
	
	upperHeight = H / 3 + 1;
	S1 = upperHeight * W;
	S2 = (H - upperHeight) * leftWidth;
	S3 = (H - upperHeight) * (W - leftWidth);
	case2 = maxmin(S1, S2, S3);
	
	if(case1 < case2){
		return case1;
	}else{
		return case2;
	}
}

int rotatedT(int H, int W){
	return T(W, H);
}


int main(void) {
	// your code goes here
	int H, W;
	scanf("%d", &H);
	scanf("%d", &W);
	
	if(H % 3 == 0 || W % 3 == 0){
		printf("0\n");
	}else{
		int min = T(H, W);
		if(min > rotatedT(H, W)){
			min = rotatedT(H, W);
		}
		if(min > H){
			min = H;
		}
		if(min > W){
			min = W;
		}
		printf("%d\n", min);
	}
	return 0;
}