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 12.16.1) (judge verdict: Wrong Answer)

//Don't have to see. start------------------------------------------
var read = require('readline').createInterface({
  input: process.stdin, output: process.stdout
});
var obj; var inLine = [];
read.on('line', function(input){inLine.push(input);});
read.on('close', function(){
  obj = init(inLine);
  console.error("\n");
  var start = Date.now();
  Main();
  var end = Date.now() - start;
  myerr("time : " + (end) + "ms");
  myerr("memory : " + Math.round(process.memoryUsage().heapTotal / 1024) + "KB");
});
function makeClone(obj){return JSON.parse(JSON.stringify(obj));}
function nextInt(){return myconv(next(),1);} function nextStrArray(){return myconv(next(),2);}
function nextIntArray(){return myconv(next(),4);} function nextCharArray(){return myconv(next(),6);}
function next(){return obj.next();} function hasNext(){return obj.hasNext();}
function init(input){  
  return {
    list : input, index : 0, max : input.length,
    hasNext : function(){return (this.index < this.max);},
    next : function(){if(this.hasNext()){return this.list[this.index++];}else{throw "ArrayIndexOutOfBoundsException ‚There is no more input";}}
  };
}
function myout(s){console.log(s);}
function myerr(s){console.error("debug:" + require("util").inspect(s,false,null));}
//param "no" is
//unknown or outlier : return i. 1: parseInt.
//2: split space. 4: split space and parseInt.
//6: split 1 character. 7: split 1 character and parseInt.
//8: join space. 9: join nextline. 0: join no character.
function myconv(i,no){try{switch(no){case 1:return parseInt(i);case 2:return i.split(" ");case 4:return i.split(" ").map(Number);case 6:return i.split("");case 7:return i.split("").map(Number);case 8:return i.join(" ");case 9:return i.join("\n");case 0:return i.join("");default:return i;}}catch(e){return i;}}

//Don't have to see. end------------------------------------------
function Main(){
  var one = nextIntArray();
  var H = one[0];
  var W = one[1];
  
  var output = 100000000000;
  for(var i = 1; i <= H - 2; i++){
    var tate1 = i;
    var tate2 = Math.floor((H - i) / 2);
    var tate3 = Math.ceil((H - i) / 2);
    var tatemax = Math.max.apply(null, [tate1, tate2, tate3]);
    var tatemin = Math.min.apply(null, [tate1, tate2, tate3]);
    output = Math.min(output, (tatemax - tatemin) * W);
    
    var yoko1 = Math.floor(W / 2);
    var yoko2 = Math.ceil(W / 2);
    var s1 = i * W;
    var s2 = (H - i) * yoko1;
    var s3 = (H - i) * yoko2;
    var yokomax = Math.max.apply(null, [s1, s2, s3]);
    var yokomin = Math.min.apply(null, [s1, s2, s3]);
    output = Math.min(output, yokomax - yokomin);
  }
  var tmp = H;
  H = W;
  W = tmp;
  for(var i = 1; i <= H - 2; i++){
    var tate1 = i;
    var tate2 = Math.floor((H - i) / 2);
    var tate3 = Math.ceil((H - i) / 2);
    var tatemax = Math.max.apply(null, [tate1, tate2, tate3]);
    var tatemin = Math.min.apply(null, [tate1, tate2, tate3]);
    output = Math.min(output, (tatemax - tatemin) * W);
    
    var yoko1 = Math.floor(W / 2);
    var yoko2 = Math.ceil(W / 2);
    var s1 = i * W;
    var s2 = (H - i) * yoko1;
    var s3 = (H - i) * yoko2;
    var yokomax = Math.max.apply(null, [s1, s2, s3]);
    var yokomin = Math.min.apply(null, [s1, s2, s3]);
    output = Math.min(output, yokomax - yokomin);
  }
  
  myout(output);
}