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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <string>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <functional>
#include <utility>
#include <tuple>
#define INF 0x3f3f3f3f
#define MOD 1000000007
#define PI 4*atan(1.0)
typedef long long ll;
typedef long double ld;
using namespace std;
int dx[4]={0,0,-1,1};
int dy[4]={-1,1,0,0};

int main(){
	ll H,W;
	cin>>H>>W;
	ll sma,big;
	ll a[5],b[5],c[5];
	ll d[5];
	if(H%3==0 || W%3==0){
		cout<<0<<endl;
		return 0;
	}
	sma=min(H,W);
	big=max(H,W);
	a[0]=(big+2)/3*sma;
	b[0]=(big-((big+2)/3))/2*sma;
	c[0]=H*W-a[0]-b[0];

	a[1]=(big)/3*sma;
	b[1]=(big-((big)/3))/2*sma;
	c[1]=H*W-a[1]-b[1];
	
	a[2]=(big+2)/3*sma;
	b[2]=(big-((big+2)/3))*(sma/2);
	c[2]=H*W-a[2]-b[2];

	a[3]=(big)/3*sma;
	b[3]=(big-((big)/3))*(sma/2);
	c[3]=H*W-a[3]-b[3];

	ll mini=INF;
	for(int i=0;i<4;i++){
		//cout<<a[i]<<" "<<b[i]<<" "<<c[i]<<endl;
		mini=min(mini,(max(a[i],max(b[i],c[i]))-(min(a[i],min(b[i],c[i])))));
	}

	swap(sma,big);
	a[0]=(big+2)/3*sma;
	b[0]=(big-((big+2)/3))/2*sma;
	c[0]=H*W-a[0]-b[0];

	a[1]=(big)/3*sma;
	b[1]=(big-((big)/3))/2*sma;
	c[1]=H*W-a[1]-b[1];
	
	a[2]=(big+2)/3*sma;
	b[2]=(big-((big+2)/3))*(sma/2);
	c[2]=H*W-a[2]-b[2];

	a[3]=(big)/3*sma;
	b[3]=(big-((big)/3))*(sma/2);
	c[3]=H*W-a[3]-b[3];

	for(int i=0;i<4;i++){
		//cout<<a[i]<<" "<<b[i]<<" "<<c[i]<<endl;
		mini=min(mini,(max(a[i],max(b[i],c[i]))-(min(a[i],min(b[i],c[i])))));
	}
	cout<<mini<<endl;
	return 0;
}