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>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <ctype.h>
#include <limits.h>	
#define inf (INT_MAX-1)
#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) qsort(a,n,sizeof(TYPE),cmp)
#define sort_r(a,n) qsort(a,n,sizeof(TYPE),cmp_r);
#define chsort(s,n) qsort(s,n,sizeof(char),cmp)
#define chsort_r(s,n) qsort(s,n,sizeof(char),char_cmp_r);
#define TYPE long long
#define MEMSET(a) memset(a,0,sizeof(a))
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;
}
long long llabs(long long a){
	return a>0?a:-a;
}
double dmax(double a,double b){
	return a>b?a:b;
}
int cmp(const void *a,const void *b){
	return *(TYPE *)a-*(TYPE *)b;
}
int cmp_r(const void *a,const void *b){
	return *(TYPE *)b-*(TYPE *)a;
}
int char_cmp(const void *a,const void *b){
	return strcmp((char *)a,(char *)b);
}
int char_cmp_r(const void *a,const void *b){
	return strcmp((char *)b,(char *)a);
}
void swap(int *a,int *b){
	int t=*a;
	*a=*b;
	*b=t;
}
long long gcd(long long x,long long y){
	return x%y?gcd(y,x%y):y;
}
long long lcm(long long x,long long y){
	return x/gcd(x,y)*y;
}
struct list{
	int a;
	struct list *prev;
	struct list *next;
};
struct list *head,*tail;
struct list *make(int a){
	struct list *p;
	p=malloc(sizeof(struct list));
	p->a=a;
	p->prev=NULL;
	p->next=NULL;
	return p;
}

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