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: Wrong Answer)

H,W=map(int, input().split())

if H%3==0 or W%3==0:
    print(0)
    exit()
elif H==2 and W==2:
    print(1)
    exit()
elif H==2 or W==2:
    smax1=2*(max(H,W)//3)
    smin1=(H*W-smax1)//2
    smax2=2*(max(H,W)//3+1)
    smin2=(H*W-smax2)//2
    #print(smax1, smin1, smax2, smin2)
    print(min(abs(smax1-smin1), abs(smax2-smin2)))
    exit()
ans=float("INF")
for t in [(H,W),(W,H)]:
    h,w=t
    first1=w*(h//3)
    sec1=(h-h//3)*(w//2)
    third1=(h-h//3)*(w-w//2)
    smax1=max(first1,sec1,third1)
    smin1=min(first1,sec1,third1)

    first2=w*(h//3+1)
    sec2=(h-h//3-1)*(w//2)
    third2=(h-h//3-1)*(w-w//2)
    smax2=max(first2,sec2,third2)
    smin2=min(first2,sec2,third2)
    sub=min(smax1-smin2, smax2-smin2)
    ans=min(sub, ans)
    #print(smin1, smax1, smin2, smax2)

print(ans)