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 Ruby (2.3.3) (judge verdict: Wrong Answer)

size = STDIN.gets.split(" ")
$h = size[0].to_i
$w = size[1].to_i

$unitPieceCount = $h * $w
$isHorizontalDivided = false

def getHalfSize(h, w)
    halfAmount = h*w/2
    
    # Vertical Division
    verticalHalf = 0
    while(verticalHalf+h <= halfAmount)
        verticalHalf = verticalHalf + h
    end
    
    # Horizontal Division
    horizontalHalf = 0
    while(horizontalHalf+w <= halfAmount)
        horizontalHalf = horizontalHalf + w
    end
    
    ary = Array.new()
    
    ary.push(horizontalHalf)
    ary.push(verticalHalf)
    
    ret = ary.min()
    if(ret == horizontalHalf)
        $isHorizontalDivided = true
    else
        $isHorizontalDivided = false
    end
    
    
    return ret
end

if($unitPieceCount % 3 == 0)
    puts "0"
elsif
    s_max = getHalfSize($h,$w)
    s_min = 0
    if($isHorizontalDivided)
        s_min = getHalfSize($h - s_max/$w, $w)
    else
        s_min = getHalfSize($h, $w - s_max/$h)
    end
    
    puts s_max - s_min
end