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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("3 1 1");
            WillReturn.Add("1 2 1");
            WillReturn.Add("2 1 2");
            WillReturn.Add("3 3 10");
            //3
            //最小予算となる組み合わせは、薬品1と薬品2を混合する場合です。
            //この場合、混合した溶液中に物質Aは3グラム、物質Bは3グラム含まれており、
            //混合比は 3:3=1:1 となって条件を満たします。
            //このときの合計価格は3円となります。
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("1 1 10");
            WillReturn.Add("10 10 10");
            //-1
            //物質Aと物質Bの混合比が1:10となる薬品の組み合わせはないので、-1を出力します
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    struct YakuhinInfoDef
    {
        internal int A;
        internal int B;
        internal int C;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();

        int[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => int.Parse(X)).ToArray();

        SplitAct(InputList[0]);
        int MA = wkArr[1];
        int MB = wkArr[2];

        var YakuhinInfoList = new List<YakuhinInfoDef>();
        foreach (string EachStr in InputList.Skip(1)) {
            SplitAct(EachStr);
            YakuhinInfoDef WillAdd;
            WillAdd.A = wkArr[0];
            WillAdd.B = wkArr[1];
            WillAdd.C = wkArr[2];
            YakuhinInfoList.Add(WillAdd);
        }

        //最小金額[タイプAの合計,タイプBの合計]なDP表
        var PrevDP = new Dictionary<string, int>();
        PrevDP["0,0"] = 0;

        foreach (YakuhinInfoDef EachYakuhin in YakuhinInfoList) {
            var CurrDP = new Dictionary<string, int>(PrevDP);
            foreach (var EachPair in PrevDP) {
                string[] CurrStr = EachPair.Key.Split(',');
                int CurrA = int.Parse(CurrStr[0]);
                int CurrB = int.Parse(CurrStr[1]);

                int NewA = CurrA + EachYakuhin.A;
                int NewB = CurrB + EachYakuhin.B;
                int NewC = EachPair.Value + EachYakuhin.C;

                string NewKey = string.Format("{0},{1}", NewA, NewB);
                if (CurrDP.ContainsKey(NewKey)) {
                    if (CurrDP[NewKey] > NewC)
                        CurrDP[NewKey] = NewC;
                }
                else CurrDP[NewKey] = NewC;
            }
            PrevDP = CurrDP;
        }

        int Answer = int.MaxValue;
        bool HasAnswer = false;

        foreach (var EachPair in PrevDP) {
            string[] wkStr = EachPair.Key.Split(',');
            int CurrA = int.Parse(wkStr[0]);
            int CurrB = int.Parse(wkStr[1]);

            for (int I = 1; I < int.MaxValue; I++) {
                if (MA * I > CurrA) break;
                if (MB * I > CurrB) break;

                if (MA * I != CurrA) continue;
                if (MB * I != CurrB) continue;

                HasAnswer = true;
                if (Answer > EachPair.Value) {
                    Answer = EachPair.Value;
                }
            }
        }
        Console.WriteLine(HasAnswer ? Answer : -1);
    }
}