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)

h,w=map(int,input().split())

if h%3==0 or w%3==0:
    print("0")
    exit()
#print(h*w)
ans=10**100**2
    #hが大きい方とみなす
if h<w:
    comp=h
    h=w
    w=comp
ans=min(ans,(h//3+1)*w-h//3*w)
#print(ans)
#print(h*w)
for i in range(1,w):
    green = h*i 
    red   = (h//2) * (w-i)
    blue  = h*w-red-green#三等分に分ける
    #print(green,red,blue)
    ma=max(green,red,blue)#一番大きい長方形
    mi=min(green,red,blue)#一番小さい長方形
    #print(green,red,blue,ma-mi)
   
    ans=min(ans,ma-mi)
comp=w
w=h
h=comp
for i in range(1,w):
    green = h*i 
    red   = (h//2) * (w-i)
    blue  = h*w-red-green#三等分に分ける
    ma=max(green,red,blue)#一番大きい長方形
    mi=min(green,red,blue)#一番小さい長方形
    #print(green,red,blue,ma-mi)
   
    ans=min(ans,ma-mi)

print(ans)