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>
using namespace std;
using ll=long long;
const ll MOD=(ll)1e9+7;

int dp[110][100][310]; //i,j,k i番目まででj個使って，重さの差の和がkの時の最大価値

ll mini(ll a,ll b,ll c){
    return min(a,min(b,c));
}

ll maxi(ll a,ll b,ll c){
    return max(a,max(b,c));
}

int main(){
    ll H,W; cin>>H>>W;
    ll ans=1e18;
    //三型
    if(H%3==0||W%3==0) ans=0;
    else ans=min(H,W);

    //T型
    ll s1,s2,s3;
    for (int i = 1; i < H; ++i) {
        s1=i*W;
        s2=(H-i)*(W/2); s3=(H-i)*W-s2;
        ans=min(ans,maxi(s1,s2,s3)-mini(s1,s2,s3));
    }

    //ト型
    for (int i = 1; i < W; ++i) {
        s1=i*H;
        s2=(W-i)*(H/2); s3=(W-i)*H-s2;
        ans=min(ans,maxi(s1,s2,s3)-mini(s1,s2,s3));
    }

    cout<<ans<<endl;

    return 0;
}