Problem:
Score : 400 points

Problem Statement

Dolphin is planning to generate a small amount of a certain chemical substance C.

In order to generate the substance C, he must prepare a solution which is a mixture of two substances A and B in the ratio of M_a:M_b.

He does not have any stock of chemicals, however, so he will purchase some chemicals at a local pharmacy.

The pharmacy sells N kinds of chemicals. For each kind of chemical, there is exactly one package of that chemical in stock.

The package of chemical i contains a_i grams of the substance A and b_i grams of the substance B, and is sold for c_i yen (the currency of Japan).

Dolphin will purchase some of these packages. For some reason, he must use all contents of the purchased packages to generate the substance C.

Find the minimum amount of money required to generate the substance C.

If it is not possible to generate the substance C by purchasing any combination of packages at the pharmacy, report that fact.

Constraints

1≦N≦40

1≦a_i,b_i≦10

1≦c_i≦100

1≦M_a,M_b≦10

gcd(M_a,M_b)=1

a_i, b_i, c_i, M_a and M_b are integers.

Input

The input is given from Standard Input in the following format:

N M_a M_b
a_1 b_1 c_1
a_2 b_2 c_2
:
a_N b_N c_N

Output

Print the minimum amount of money required to generate the substance C. If it is not possible to generate the substance C, print -1 instead.

Sample Input 1

3 1 1
1 2 1
2 1 2
3 3 10

Sample Output 1

3

The amount of money spent will be minimized by purchasing the packages of chemicals 1 and 2.

In this case, the mixture of the purchased chemicals will contain 3 grams of the substance A and 3 grams of the substance B, which are in the desired ratio: 3:3=1:1.

The total price of these packages is 3 yen.

Sample Input 2

1 1 10
10 10 10

Sample Output 2

-1

The ratio 1:10 of the two substances A and B cannot be satisfied by purchasing any combination of the packages. Thus, the output should be -1.

Solution in JavaScript (node.js v5.12) (judge verdict: Runtime Error)

var obj = init();
Main();
function nextInt(){return myconv(next(),1);}
function nextStrArray(){return myconv(next(),2);}//半角スペース分割
function nextIntArray(){return myconv(next(),4);}//半角スペース + 数値化
function nextCharArray(){return myconv(next(),6);}//1文字分割
function next(){return obj.next();}
function hasNext(){return obj.hasNext();}
function myin(){return require("fs").readFileSync("/dev/stdin", "utf8").trim().split("\n");}
function init(){
  var inputFile = myin();
  var returnObj = {
    "list" : inputFile, "index" : 0, "max" : inputFile.length,
    "hasNext" : function(){return (this.index < this.max);},
    "next" : function(){if(!this.hasNext()){throw "ArrayIndexOutOfBoundsException これ以上ないよ";}else{var returnInput = this.list[this.index];this.index++;return returnInput;}}
  };
  return returnObj;
}
function myout(t){console.log(t);}//標準出力
function myerr(t){console.error(t);}//標準エラー出力
//[no]要素の扱い。数値型
//不明値、異常時:引数そのまま返す　1:数値へ変換
//2:半角SPで分割 4:半角SPで分割し、数値配列へ
//6:1文字で分割  7:1文字で分割し、数値配列へ
//8:半角SPで結合 9:改行で結合 0:文字なしで結合
function myconv(i,no){try{switch(no){case 1:return parseInt(i);case 2:return i.split(" ");case 4:return i.split(" ").map((a)=>Number(a));case 6:return i.split("");case 7:return i.split("").map((a)=>Number(a));case 8:return i.join(" ");case 9:return i.join("\n");case 0:return i.join("");default:return i;}}catch(e){return i;}}
function Main(){
  var one = nextIntArray();
  var N = one[0];
  var MA = one[1];
  var MB = one[2];
  var list = new Array(N);
  for(var i = 0; i < N; i++){
    list[i] = nextIntArray();
  }
  var dp = new Array(N + 1);
  var maxValue = 101;
  for(var i = 0; i < N + 1; i++){
    dp[i] = new Array(maxValue);
    for(var j = 0; j < maxValue; j++){
      dp[i][j] = new Array(maxValue);
    }
  }
  dp[0][0][0] = 0;
  //dp[i][j][k] : i個目を買い、MA合計がj、MB合計がkになる時の最小コスト
  for(var i = 1; i <= N; i++){
	for(var j = 0; j < maxValue; j++){
		for(var k = 0; k < maxValue; k++){
			if(dp[i - 1][j][k] != null){
				dp[i][j][k] = dp[i - 1][j][k];
			}
		}
		
	}
    var item = list[i - 1];
    for(var j = 0; j < maxValue; j++){
      for(var k = 0; k < maxValue; k++){
        //myerr({i,j,k});
        if(dp[i - 1][j][k] != null){
          if(dp[i][j + item[0]][k + item[1]] == null){
            dp[i][j + item[0]][k + item[1]] = dp[i - 1][j][k] + item[2];
          }else{
            dp[i][j + item[0]][k + item[1]] = Math.min(dp[i - 1][j][k] + item[2], dp[i][j + item[0]][k + item[1]]);
          }
        }
      }
    }
  }
	var count = 1;
	var output = 10000;
	while(true){
		var getMA = MA * count;
		var getMB = MB * count;
		if(getMA < maxValue && getMB < maxValue){
			if(dp[N][getMA][getMB] != null){
				output = Math.min(output,dp[N][getMA][getMB]);
			}
		}else{
			break;
		}
		count++;
	}
	if(output == 10000){
		myout(-1);
	}else{
		myout(output);
	}
}