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 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <algorithm>
#include <iomanip>
#include <math.h>
#include <string.h>
#include <cstdio>
#include <tuple>
#include <numeric>
using namespace std; using ll = long long; using ld = long double;  using pll = pair<ll, ll>;
using vl = vector<ll>; using vll = vector<vl>; using vpll = vector<pll>;
using vs = vector<string>; using tll = tuple<ll, ll, ll>; using vtll = vector<tll>;
const ld PI = 3.1415926535897932;
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define co(i) cout << i << endl;
#define co2(i,j) cout << i << " " << j << endl;
#define co3(i) cout << i << " ";
#define po(i) cout << i.first << " " << i.second << endl;
void in() {}
void debug_out() { cerr << endl; }
template<typename Head, typename... Tail>
void debug_out(Head h, Tail... t) {
	cerr << " " << h;
	if (sizeof...(t) > 0) cerr << " :";
	debug_out(t...);
}
template <typename T>
ostream& operator<<(ostream& os, vector<T> vec) {
	for (size_t i = 0; i < vec.size(); i++)os << vec[i] << (i + 1 == vec.size() ? "" : " ");
	return os;
}
ll ctoi(char c) {
	switch (c) {
	case '0': return 0; case '1': return 1; case '2': return 2;
	case '3': return 3; case '4': return 4; case '5': return 5;
	case '6': return 6; case '7': return 7; case '8': return 8;
	case '9': return 9;  default: return 0;
	}
}
bool pairCompare(const pll firstElof, pll secondElof)
{
	return firstElof.first > secondElof.first;
}
//**Snippetリスト**//
//rep, vin, all, iteLoop, bitSearch, bitList, nod, digitDP, treeDP//
//gcdlcm, isPrime, eratos, primeFactorize, Npow, combination, divisor, modinv, doubling//
//dfs, bfs, dijkstra, WarshallFloyd, BellmanFord, UnionFind, Kruskal, RMQ, LCA//
ll i, j, k, l; ll N, M, K, H, W, L, X, Y, Z, R, Q;
ll MOD = 1000000007, INF = 1LL << 60, ans = 0, z = 0, o = 1;
vll flag, D; vll path;
//***********//
int main() {
	cin >> H >> W;
	ans = INF;
	for (i = 1; i <= H - 1; i++) {
		ll A = i * W;
		ll B = (H - i) * (W / 2);
		ll C = H * W - A - B;
		ll D = D = max(abs(A - B), max(abs(A - C), abs(B - C)));
		ans = min(ans, D);
		B = ((H - i) / 2) * W;
		C = H * W - A - B;
		D = max(abs(A - B), max(abs(A - C), abs(B - C)));
		ans = min(ans, D);
	}
	for (j = 1; j <= W - 1; j++) {
		ll A = H * j;
		ll B = H / 2 * (W - j);
		ll C = H * W - A - B;
		ll D = D = max(abs(A - B), max(abs(A - C), abs(B - C)));
		ans = min(ans, D);
		B = H * ((W - j) / 2);
		C = H * W - A - B;
		D = max(abs(A - B), max(abs(A - C), abs(B - C)));
		ans = min(ans, D);
	}
	co(ans);
}