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)

import math

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

ans=H*W
for i in range(1,H):
	s=i*W
	h=H-i
	t1=(h//2)*W
	t2=math.ceil(h/2)*W
	if all([s,t1,t2]):
		ans=min(ans, max(s,t1,t2)-min(s,t1,t2))
	
	t1=(W//2)*h
	t2=math.ceil(W/2)*h
	if all([s,t1,t2]):
		ans=min(ans, max(s,t1,t2)-min(s,t1,t2))

for i in range(1,W):
	s=i*H
	w=W-i
	t1=(w//2)*H
	t2=math.ceil(w/2)*H
	if all([s,t1,t2]):
		ans=min(ans, max(s,t1,t2)-min(s,t1,t2))
	
	t1=(H//2)*w
	t2=math.ceil(H/2)*w
	if all([s,t1,t2]):
		ans=min(ans, max(s,t1,t2)-min(s,t1,t2))

print(ans)