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 <limits.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>
#include <math.h>

#define P 1000000007

int comp(const void *a, const void *b){return *(int*)a-*(int*)b;}

inline long ab(long a, long b){return a>b?a-b:b-a;}

int main(void){
	int h, w, i;
	scanf("%d%d", &h, &w);
	
	long ans=((long)h)*w;
	for(i=0; i<=w; i++){
		long a1 = ((long)h)*(w-i);
		long now;
		if(h%2==0 || i%2==0){
			long a2 = ((long)h)*i/2;
			now = ab(a1, a2);
		}else{
			long a2, a3;
			if(h<i){
				a2 = ((long)h)*(i/2);
				a3 = ((long)h)*((i+1)/2);
			}else{
				a2 = ((long)h/2)*i;
				a3 = ((long)(h+1)/2)*i;
			}
			long b1 = ab(a1, a2);
			long b2 = ab(a2, a3);
			long b3 = ab(a3, a1);
			now = b1<b2?b2<b3?b3:b2:b1<b3?b3:b1;
		}
		if(now<ans) ans=now;
	}
	for(i=0; i<=h; i++){
		long a1 = ((long)w)*(h-i);
		long now;
		if(w%2==0 || i%2==0){
			long a2 = ((long)w)*i/2;
			now = ab(a1, a2);
		}else{
			long a2, a3;
			if(w<i){
				a2 = ((long)w)*(i/2);
				a3 = ((long)w)*((i+1)/2);
			}else{
				a2 = ((long)w/2)*i;
				a3 = ((long)(w+1)/2)*i;
			}
			long b1 = ab(a1, a2);
			long b2 = ab(a2, a3);
			long b3 = ab(a3, a1);
			now = b1<b2?b2<b3?b3:b2:b1<b3?b3:b1;
		}
		if(now<ans) ans=now;
	}
	printf("%ld\n", ans);
}