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)

temp=input().split()
H=int(temp[0])
W=int(temp[1])

INF=10000000000
ans=INF
#超特殊例
if H%3==0 or W%3==0:
	ans=0
ans=min(ans,H,W)
#横長がある場合
for i in range(H):
	S1=W*i
	S2=int(W/2)*(H-i)
	S3=(W-int(W/2))*(H-i)
	if max(S1,S2,S3)-min(S1,S2,S3)<ans:
		ans=max(S1,S2,S3)-min(S1,S2,S3)
for i in range(W):
	S1=H*i
	S2=int(H/2)*(W-i)
	S3=(H-int(H/2))*(W-i)
	if max(S1,S2,S3)-min(S1,S2,S3)<ans:
		ans=max(S1,S2,S3)-min(S1,S2,S3)
print(ans)