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>
#include<math.h>
#define FOR(i,a,b) for(int i=a;i<b;i++)
#define lln long long int

int main(){

	lln h,w;
	lln small,big;
	lln A,B,C;
	lln small2,big2;
	lln min;

	scanf("%lld %lld",&h,&w);
	small = fmin(h,w);
	big = fmax(h,w);

	if(small % 3 == 0 || big % 3 == 0){
		printf("0\n");
		return 0;
	}

	min = small;

	FOR(i,1,big+1){
		A = i*small;

		if(small % 2 == 0){
			B = (big - i) * (small / 2);
			C = B;
		}else{
			B = (big - i) * ((small+1) / 2);
			C = B - (big - i);
		}

//		printf("%lld %lld %lld\n",A,B,C);

		big2 = fmax(A,B);
		small2 = fmin(A,C);
//		printf("%lld %lld\n",big2,small2);

		if(min > fmin(small, big2-small2)){
			min = fmin(small, big2-small2);
		}
	}

	printf("%lld\n",min);
}