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 Python (3.8.2) (judge verdict: Accepted)

import sys
import itertools
# import numpy as np
import time
import math
import heapq
from collections import defaultdict
sys.setrecursionlimit(10 ** 7)
 
INF = 10 ** 18
MOD = 10 ** 9 + 7
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

# map(int, input().split())

H, W = map(int, input().split())
if H > W:
    H, W = W, H

S = H * W

ans = INF
for i in range(1, H + 1):
    a = i * W
    h = H - i
    w = W
    remain = S - a
    b = h * (w // 2)
    c = remain - b
    ans = min(ans, max(a, b, c) - min(a, b, c))
    b = w * (h // 2)
    c = remain - b
    ans = min(ans, max(a, b, c) - min(a, b, c))
for i in range(1, W + 1):
    a = i * H
    h = H
    w = W - i
    remain = S - a
    b = h * (w // 2)
    c = remain - b
    ans = min(ans, max(a, b, c) - min(a, b, c))
    b = w * (h // 2)
    c = remain - b
    ans = min(ans, max(a, b, c) - min(a, b, c))
print(ans)