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 <stdlib.h>
#include <string.h>
#include <math.h>
#include <ctype.h>
#include <limits.h>	
#define inf INT_MAX
#define INF 9223372036854775807
#define sq(n) ((n)*(n))
#define rep(i,n) for(i=0;i<n;i++)
#define rev(i,n) for(i=n-1;i>=0;i--)
#define sort(a,n,type) qsort(a,n,sizeof(type),cmp)
const int mod=(int)1e09+7;

int in(void){
	int i;scanf("%d",&i);
	return i;
}
long long llin(void){
	long long i;scanf("%lld",&i);
	return i;
}
double din(void){
	double i;scanf("%lf",&i);
	return i;
}
void chin(char s[]){
	scanf("%s",s);
}
void print(int a){
	printf("%d\n",a);
}
void llprint(long long a){
	printf("%lld\n",a);
}
void dprint(double a){
	printf("%.10f\n",a);
}
void print2(int a,int b){
	printf("%d %d\n",a,b);
}
long long max(long long a,long long b){
	return a>b?a:b;
}
long long min(long long a,long long b){
	return a<b?a:b;
}
double dmax(double a,double b){
	return a>b?a:b;
}
int cmp(const void *a,const void *b){
	return *(long long *)a-*(long long *)b;
}

int main(void){
	long long h=llin(),w=llin(),i,ans=10000000000,t[3];
	for(i=1;i<h;i++){
		t[0]=i*w;
		t[1]=(h-i)*(w/2);
		t[2]=(h-i)*((w+1)/2);
		sort(t,3,long long);
		ans=min(ans,t[2]-t[0]);
		t[0]=i*w;
		t[1]=((h-i)/2)*w;
		t[2]=((h-i+1)/2)*w;
		sort(t,3,long long);
		ans=min(ans,t[2]-t[0]);
	}
	for(i=1;i<w;i++){
		t[0]=i*h;
		t[1]=(w-i)*(h/2);
		t[2]=(w-i)*((h+1)/2);
		sort(t,3,long long);
		ans=min(ans,t[2]-t[0]);
		t[0]=i*h;
		t[1]=((w-i)/2)*h;
		t[2]=((w-i+1)/2)*h;
		sort(t,3,long long);
		ans=min(ans,t[2]-t[0]);
	}
	llprint(ans);
	return 0;
}