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: Runtime Error)

H,W = map(int,input().split())
min_tmp=1000000

if H%3 == 0 or W%3 == 0:
    print(0)

else:
    for i in range(W):#縦方向に可変なバーを作成
        a1 = i*H      #左側面積
        a2 = (W-i)*H  #右側面積
        if a1 > a2: #左側面積のほうが大きいとき
            for j in range(i):#さらに縦割り
                a3 = i*H      #左側面積
                a4 = (i-j)*H  #真ん中面積
                a5 = (W-i)*H  #右側面積
                a6 = max(a3,a4,a5)-min(a3,a4,a5)
                if a6 < min_tmp: min_tmp = a6
            for k in range(H):#今度は横割
                a7 = k*i      #上側面積
                a8 = (H-k)*i  #下側面積
                a9 = max(a1,a2,a7,a8)-min(a1,a2,a7,a8)
                if a9 < min_tmp: min_tmp = a9
        else :
            for j in range(i:W):#さらに縦割り
                a3 = i*H      #左側面積
                a4 = (i-j)*H  #真ん中面積
                a5 = (W-i)*H  #右側面積
                a6 = max(a3,a4,a5)-min(a3,a4,a5)
                if a6 < min_tmp: min_tmp = a6
            for k in range(H):#今度は横割
                a7 = k*i      #上側面積
                a8 = (H-k)*i  #下側面積
                a9 = max(a1,a2,a7,a8)-min(a1,a2,a7,a8)
                if a9 < min_tmp: min_tmp = a9
    print(min_tmp)