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<bits/stdc++.h>
#define LL long long
#define REP(i,n) for(int i=0;i<(n);++i)
#define PER(i,n) for(int i=n-1;i>=0;--i)
#define REPA(i,n) for(int i=1;i<(n);++i)
#define foreach(i, n) for(auto &i:(n))
#define PII pair<int,int>
#define PLI pair<long long, int>
#define PLL pair<long long, long long>
#define MOD ((LL)1e9+7) 
#define INF ((int)1e9+7)
#define INFLL ((LL)1e18)
#define ALL(x) (x).begin(),(x).end()
#define BIT(x) (1LL << (x))
using namespace std;

LL modpow(LL x, LL b){
	LL res = 1;
	while(b){
		if(b&1)res = res * x % MOD;
		x = x * x % MOD;
		b>>=1;
	}
	return res;
}

LL modinv(LL x){
	return modpow(x, MOD-2);
}

int main(){
	LL H, W;
	cin >> H >> W;
	LL ans = INF;
	REP(i, H/2+1){
		LL a = i * W;
		LL b = (H-i)/2 * W;
		LL c = (H-i+1)/2 * W;
		ans = min(ans, max({a, b, c}) - min({a, b, c}));
		b = (H-i) * (W / 2);
		c = (H-i) * ((W+1) / 2);
		ans = min(ans, max({a, b, c}) - min({a, b, c}));
	}
	REP(i, W/2+1){
		LL a = H * i;
		LL b = H * ((W-i)/2);
		LL c = H * ((W-i+1)/2);
		ans = min(ans, max({a, b, c}) - min({a, b, c}));
		b = (H/2) * (W-i);
		c = ((H+1)/2) * (W-i);
		ans = min(ans, max({a, b, c}) - min({a, b, c}));
	}
	cout << ans << endl;
	return 0;
}