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 (3.4.3) (judge verdict: Accepted)

# coding: utf-8
# hello worldと表示する
import sys
import numpy
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import Counter, deque
from collections import defaultdict
from itertools import combinations, permutations, accumulate, groupby, product
from bisect import bisect_left,bisect_right
from heapq import heapify, heappop, heappush
from math import floor, ceil,pi,factorial
from operator import itemgetter
from copy import deepcopy
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))
def LI2(): return [int(input()) for i in range(n)]
def MXI(): return [[LI()]for i in range(n)]
def SI(): return input().rstrip()
def printns(x): print('\n'.join(x))
def printni(x): print('\n'.join(list(map(str,x))))
inf = 10**17
mod = 10**9 + 7

h,w=MI()
if w%3==0:
    s1=0
else:
    s1=h
if h%3==0:
    s2=0
else:
    s2=w
fw=floor(w/3)
fh=floor(h/2)
cw=ceil(w/3)
SMAX1=(w-fw)*(h-fh)
SMIN1=min(fw*h,(w-fw)*fh)
SMAX2=max(cw*h,(w-cw)*(h-fh))
SMIN2=(w-cw)*fh
#print(SMAX1,SMIN1,SMAX2,SMIN2)
s3=min(SMAX1-SMIN1,SMAX2-SMIN2)
h,w=w,h
fw=floor(w/3)
fh=floor(h/2)
cw=ceil(w/3)
SMAX1=(w-fw)*(h-fh)
SMIN1=min(fw*h,(w-fw)*fh)
SMAX2=max(cw*h,(w-cw)*(h-fh))
SMIN2=(w-cw)*fh
s4=min(SMAX1-SMIN1,SMAX2-SMIN2)
#print(s1,s2,s3,s4)
ans=min(s1,s2,s3,s4)
print(ans)