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 <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdbool.h>
#include <math.h>

long long max(long long a, long long b, long long c){
    if(a >= b && a >= c){
        return a;
    }else if(b >= a && b >= c){
        return b;
    }else{
        return c;
    }
}

long long min(long long a, long long b, long long c){
    if(a <= b && a <= c){
        return a;
    }else if(b <= a && b <= c){
        return b;
    }else{
        return c;
    }
}

int main(void){

    long long H, W;

    scanf("%lld%lld", &H, &W);

    long long a, b, c;
    long long ans = H * W;

    for(int i = 1; i <= W-1; i++){
        a = H * i;
        b = H * ((W-i)/2);
        c = H * W - a - b;
        if(max(a,b,c) - min(a,b,c) < ans){
            ans = max(a,b,c) - min(a,b,c);
        }
        b = (W-i) * (H/2);
        c = H * W - a - b;
        if(max(a,b,c) - min(a,b,c) < ans){
            ans = max(a,b,c) - min(a,b,c);
        }
    }

    for(int i = 1; i <= H-1; i++){
        a = W * i;
        b = W * ((H-i)/2);
        c = H * W - a - b;
        if(max(a,b,c) - min(a,b,c) < ans){
            ans = max(a,b,c) - min(a,b,c);
        }
        b = (H-i) * (W/2);
        c = H * W - a - b;
        if(max(a,b,c) - min(a,b,c) < ans){
            ans = max(a,b,c) - min(a,b,c);
        }
    }

    printf("%lld\n", ans);

    return 0;
}