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: Wrong Answer)

#include <iostream>
#include <vector>
#include <algorithm>
#include <iomanip>
#include <queue>
#include <string>
#include <utility>
#include <map>
using namespace std;
#define rep(i,n) for(int i=1;i<=(int)(n);i++)
#define Rep(i,n) for(int i=0;i<=(int)(n-1);i++)
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pint;
typedef pair<ll,ll> pll;
typedef map<int,int> mint;
int dx[4]={-1,0,1,0};
int dy[4]={0,-1,0,1};
int inf=1e9+100;
ll infi =1e18+100;

ll H,W;

int main() {
	cin>>H>>W;
	if(H%3==0||W%3==0) cout<<0<<endl;
	else{
		if(H>W){
			swap(H,W);
		}
		if(H==1) cout<<1<<endl;
		else{
		ll ans=infi;
		rep(i,W-1){
			ll p=abs(H*i-(H/2)*(W-i));
			ll q=abs(H*i-(((H+1)/2)*(W-i)));
			if(p<q) swap(p,q);
			if(p<ans) ans=p;
		}
	}
	}
	


	return 0;
}