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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <string.h>
#include <math.h>
#define REP(i, n) for (ll i = 0; i < n; i++)
#define REP1(i, n) for (ll i = 1; i <= n; i++)
#define RREP(i, n) for (ll i = n - 1; i >= 0; i--)
#define RREP1(i, n) for (ll i = n; i >= 1; i--)
#define FOR(i, a, b, c) for (ll i = a; i <= b; i += c)
#define RFOR(i, a, b, c) for (ll i = a; i >= b; i -= c)
#define MAX(a, b) (a > b ? a : b)
#define MIN(a, b) (a < b ? a : b)
#define INF 1145141919
typedef long long ll;
 
int main() {
    ll h, w;
    scanf("%lld %lld", &h, &w);
    
    if (h % 3 == 0 || w % 3 == 0) {
        puts("0");
        return 0;
    }
    ll min = (ll)INF * INF;
    {
        ll t1 = h * (w / 3);
        ll t2 = h * ((w - (w / 3)) / 2);
        ll t3 = (h * w) - t1 - t2;
        ll tmax = MAX(MAX(t1, t2), t3);
        ll tmin = MIN(MIN(t1, t2), t3);
        min = MIN(min, tmax - tmin);
    }
    {
        ll t1 = w * (h / 3);
        ll t2 = w * ((h - (h / 3)) / 2);
        ll t3 = (h * w) - t1 - t2;
        ll tmax = MAX(MAX(t1, t2), t3);
        ll tmin = MIN(MIN(t1, t2), t3);
        min = MIN(min, tmax - tmin);
    }
    REP(i, h + 1) {
        ll t1 = w * i;
        ll t2 = (h - i) * (w / 2);
        ll t3 = w % 2 == 0 ? t2 : t2 + (h - i);
        ll tmax = MAX(MAX(t1, t2), t3);
        ll tmin = MIN(MIN(t1, t2), t3);
        min = MIN(min, tmax - tmin);
    }
    REP(i, w + 1) {
        ll t1 = h * i;
        ll t2 = (w - i) * (h / 2);
        ll t3 = h % 2 == 0 ? t2 : t2 + (w - i);
        ll tmax = MAX(MAX(t1, t2), t3);
        ll tmin = MIN(MIN(t1, t2), t3);
        min = MIN(min, tmax - tmin);
    }
    printf("%lld\n", min);
    return 0;
}