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)

#pragma region include
#include <iostream>
#include <iomanip>
#include <stdio.h>

#include <sstream>
#include <algorithm>
#include <cmath>
#include <complex>

#include <string>
#include <cstring>
#include <vector>
#include <tuple>

#include <queue>
#include <complex>
#include <set>
#include <map>
#include <stack>
#include <list>

#include <fstream>
#include <random>
//#include <time.h>
#include <ctime>
#pragma endregion //#include
/////////
#define REP(i, x, n) for(int i = x; i < n; ++i)
#define rep(i,n) REP(i,0,n)
/////////
#pragma region typedef
typedef long long LL;
typedef long double LD;
typedef unsigned long long ULL;
#pragma endregion //typedef
////定数
const int INF = (int)1e9;
const LL MOD = (LL)1e9+7;
const LL LINF = (LL)1e18;
const double PI = acos(-1.0);
const double EPS = 1e-9;
/////////
using namespace::std;
//ex
void solve(){
	LL H,W;
	cin >> H >> W;

	LL ans = LINF;
	LL MIN = LINF;
	LL MAX = -LINF;
	LL A,B,C;
	LL Left,Right;

	Left = W*(H/2)/(H+(H/2));
	Right = W*(H-(H/2))/(2*H-(H/2));
	if( Left < Right ){
		swap(Left,Right);
	}
	Left = max(Left-1,(LL)0);
	Right = min( Right+1,W);
	for(LL w=Left;w<=Right;++w){
		vector<LL> temp(3);
		temp[0] = (W-w)*(H/2);
		temp[1] = (W-w)*(H-(H/2));
		temp[2] = w*H;
		sort(temp.begin(), temp.end());
		ans = min( ans, temp[2]-temp[0]);

		temp[0] = H*((W-w)/2);
		temp[1] = H*((W-w)-((W-w)/2));
		temp[2] = w*H;
		sort( temp.begin(), temp.end() );
		ans = min(ans,temp[2]-temp[0]);
	}
		
	swap(H,W);
	Left = W*(H/2)/(H+(H/2));
	Right = W*(H-(H/2))/(2*H-(H/2));
	if( Left < Right ){
		swap(Left,Right);
	}
	Left = max(Left-1,(LL)0);
	Right = min( Right+1,W);
	for(LL w=Left;w<=Right;++w){
		vector<LL> temp(3);
		temp[0] = (W-w)*(H/2);
		temp[1] = (W-w)*(H-(H/2));
		temp[2] = w*H;
		sort(temp.begin(), temp.end());
		ans = min( ans, temp[2]-temp[0]);

		temp[0] = H*((W-w)/2);
		temp[1] = H*((W-w)-((W-w)/2));
		temp[2] = w*H;
		sort( temp.begin(), temp.end() );
		ans = min(ans,temp[2]-temp[0]);
	}
	cout << ans << endl;
}

#pragma region main
signed main(void){
	std::cin.tie(0);
	std::ios::sync_with_stdio(false);
	std::cout << std::fixed;//小数を10進数表示
	cout << setprecision(3);//小数点以下の桁数を指定//coutとcerrで別	
	
	solve();
}
#pragma endregion //main()