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 PHP (7.4.4) (judge verdict: Accepted)

<?php
  list($h, $w) = explode(" ", trim(fgets(STDIN)));

  $ans = PHP_INT_MAX;
  // 横に3つ分ける場合
  $min = intdiv($h, 3);
  $max = intdiv($h+3-1, 3);
  $ans = min($ans, $max*$w - $min*$w);

  // 縦に３つ分ける場合
  $min = intdiv($w, 3);
  $max = intdiv($w+3-1, 3);
  $ans = min($ans, $max*$h - $min*$h);

  // 縦に１つ、横に２つ分ける場合
  // 縦が大きい
  $w1 = intdiv($w+3-1, 3);
  $w2=$w-$w1;
  $h1=intdiv($h, 2);
  $h2=$h-$h1;
  $ans = min($ans, max($h1*$w2, $h2*$w2, $h*$w1)-min($h1*$w2, $h2*$w2, $h*$w1));

  // 縦が小さい
  $w1 = intdiv($w, 3);
  $w2=$w-$w1;
  $h1=intdiv($h, 2);
  $h2=$h-$h1;
  $ans = min($ans, max($h1*$w2, $h2*$w2, $h*$w1)-min($h1*$w2, $h2*$w2, $h*$w1));

  // 横に１つ、縦に２つ分ける場合
  // 横が大きい
  $h1 = intdiv($h+3-1, 3);
  $h2=$h-$h1;
  $w1=intdiv($w, 2);
  $w2=$w-$w1;
  $ans = min($ans, max($h1*$w, $h2*$w2, $h2*$w1)-min($h1*$w, $h2*$w2, $h2*$w1));

  // 横が小さい
  $h1 = intdiv($h, 3);
  $h2=$h-$h1;
  $w1=intdiv($w, 2);
  $w2=$w-$w1;
  $ans = min($ans, max($h1*$w, $h2*$w2, $h2*$w1)-min($h1*$w, $h2*$w2, $h2*$w1));

  echo $ans;