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 Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use {
   proconio::{fastout, input, marker::*},
   std::cmp::*,
   std::collections::*,
};

macro_rules !min {($a :expr $(,) *) =>{{$a } } ;($a :expr ,$b :expr $(,) *) =>{{std ::cmp ::min ($a ,$b ) } } ;($a :expr ,$($rest :expr ) ,+$(,) *) =>{{std ::cmp ::min ($a ,min !($($rest ) ,+) ) } } ;}
macro_rules !max {($a :expr $(,) *) =>{{$a } } ;($a :expr ,$b :expr $(,) *) =>{{std ::cmp ::max ($a ,$b ) } } ;($a :expr ,$($rest :expr ) ,+$(,) *) =>{{std ::cmp ::max ($a ,max !($($rest ) ,+) ) } } ;}

#[fastout]
fn main() {
   input! {
      h: i64,
      w: i64
   }

   if h % 3 == 0 || w % 3 == 0 {
      println!("0");
      return;
   }

   let mut ans = min(h, w);
   let w1 = w / 2;
   let w2 = w - w / 2;
   for h1 in 1..h {
      let h2 = h - h1;
      let s1 = max! {h1*w, h2*w1, h2*w2};
      let s2 = min! {h1*w, h2*w1, h2*w2};
      ans = std::cmp::min(ans, (s1 - s2).abs());
   }
   let h1 = h / 2;
   let h2 = h - h / 2;
   for w1 in 1..w {
      let w2 = w - w1;
      let s1 = max! {h*w1, h1*w2, h2*w2};
      let s2 = min! {h*w1, h1*w2, h2*w2};
      ans = std::cmp::min(ans, (s1 - s2).abs());
   }
   println!("{}", ans);
}