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 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#define ll long long int

ll M(ll a, ll b, ll c){
    return a > b ? a > c ? a : c : b > c ? b: c;
}

ll m(ll a, ll b, ll c){
    return a < b ? a < c ? a : c : b < c ? b : c;
}
int main(){
    ll i, j, h ,w, ans = 0;
    ll s, t, u, v;
    scanf("%lld%lld", &h, &w);
    
    if(h % 3 == 0 || w % 3 == 0){
        printf("0\n");
        return 0;
    }
    
    //縦横最小
    ans = w < h ? w: h;
    
    //縦横１個ずつ
    for(i = 1; i <= h / 2; i++){
        s = w * i;
        //1
        t = (h - i) * (s / (h - i));
        u = (h - i) * (w - (s / (h - i)));
        v = M(s, t, u) - m(s, t, u);
        printf("%d %d %d %d \n", s, t, u, v);
        if(v == 0){
            printf("0\n");
            return 0;
        }
        if(ans > v) ans = v;
        
        //2
        t = (h - i) * (w / 2);
        u = (h - i) * (w - (w / 2));
        v = M(s, t, u) - m(s, t, u);
        if(v == 0){
            printf("0\n");
            return 0;
        }
        if(ans > v) ans = v;
    }
    
    for(i = 1; i <= w / 2; i++){
        s = i * i;
        //1
        t = (w - i) * (s / (w - i));
        u = (w - i) * (h - (s / (w - i)));
        v = M(s, t, u) - m(s, t, u);
        if(v == 0){
            printf("0\n");
            return 0;
        }
        if(ans > v) ans = v;
        
        //2
        t = (w - i) * (h / 2);
        u = (w - i) * (h - (h /2));
        v = M(s, t, u) - m(s, t, u);
        if(v == 0){
            printf("0\n");
            return 0;
        }
        if(ans > v) ans = v;
    }
    printf("%lld\n", ans);
    return 0;
}