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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    let H = parseInt(arg[0].split(" ")[0]);
    let W = parseInt(arg[0].split(" ")[1]);
    
    let answer = H * W;
    let s = [...Array(3)];
    
    for(let i=0; i<2; i++) {
        for(let h=1; h<H; h++) {
            // 縦割り
            s[0] = h * W;
            s[1] = (H - h) * (W / 2);
            s[2] = H * W - (s[0] + s[1]);
            
            s.sort((a,b)=>a-b);
            answer = Math.min(answer, s[2] - s[0]);
            
            // 横割り
            s[0] = h * W;
            s[1] = ((H - h) / 2) * W;
            s[2] = H * W - (s[0] + s[1]);
            
            s.sort((a,b)=>a-b);
            answer = Math.min(answer, s[2] - s[0]);
        }
        
        // 90度回転
        let temp = H;
        H = W;
        W = temp;
    }
    
    console.log(answer);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));