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 Lua (5.3.2) (judge verdict: Accepted)

local DBG = true
local function dbgpr(...)
    if DBG then
        io.write("[dbg]")
        print(...)
    end
end
local function dbgpr_t(tbl, use_pairs)
    if DBG then
        local enum = ipairs
        if use_pairs then
            enum = pairs
        end
        dbgpr(tbl)
        io.write("[dbg]")
        for i,v in enum(tbl) do
            io.write(i)
            io.write(":")
            io.write(tostring(v))
            io.write(" ")
        end
        print("")
    end
end
local H, W = io.read("n", "n")
local INF = 99999999999
local function vert()
    local m = W % 3
    if m == 0 then
        return 0
    else
        return H
    end
end

local function horiz()
    local m = H % 3
    if m == 0 then
        return 0
    else
        return W
    end
end

local function maxmindiff(a,b,c)
    local max = math.max(a,b,c)
    local min = math.min(a,b,c)
    return max - min
end

local function vh()
    local d = W // 3
    local dd = H // 2
    local ans = INF
    for w=math.max(d-3,0),math.min(d+3,W) do
        local area1 = w * H
        for h=math.max(dd-3,0),math.min(dd+3,H) do
            local area2 = (W - w) * h
            local area3 = (W - w) * (H - h)
            ans = math.min(ans, maxmindiff(area1,area2,area3))
        end
    end
    return ans
end


local function hv()
    local d = H // 3
    local dd = W // 2
    local ans = INF
    for h=math.max(d-3,0),math.min(d+3,H) do
        local area1 = h * W
        for w=math.max(dd-3,0),math.min(dd+3,W) do
            local area2 = (H - h) * w
            local area3 = (H - h) * (W - w)
            ans = math.min(ans, maxmindiff(area1,area2,area3))
        end
    end
    return ans
end

local answers = {vert(), horiz(), vh(), hv()}
--dbgpr_t(answers)
print(math.min(table.unpack(answers)))