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;

public static partial class Program
{
    public static void Main()
    {
        var nab = CRL().ArrayInts();
        var n = nab[0];
        var ma = nab[1];
        var mb = nab[2];
        var a = new int[n];
        var b = new int[n];
        var c = new int[n];

        for (int i = 0; i < n; i++)
        {
            var input = CRL().ArrayInts();
            a[i] = input[0];
            b[i] = input[1];
            c[i] = input[2];
        }

        var max = Math.Max(a.Max(), b.Max());

        // dp[i, ca, cb]
        // 1 -> i + 1番目までの薬品の組み合わせで、a == ca, b == cbになる時の最小コスト
        var dp = new int[n + 1, n * max + 1, n * max + 1];
        for (int i = 0; i < n + 1; i++)
        {
            for (int j = 0; j < n * max + 1; j++)
            {
                for (int k = 0; k < n * max + 1; k++)
                {
                    dp[i, j, k] = int.MaxValue;
                }
            }
        }

        dp[0, 0, 0] = 0;

        for (int i = 0; i < n; i++)
        {
            for (int ca = 0; ca < n * max; ca++)
            {
                for (int cb = 0; cb < n * max; cb++)
                {
                    if (dp[i, ca, cb] == int.MaxValue)
                    {
                        continue;
                    }

                    //i + 1番目の薬品を加えない場合
                    dp[i + 1, ca, cb] = Math.Min(dp[i + 1, ca, cb], dp[i, ca, cb]);

                    //i + 1番目の薬品を加える場合
                    dp[i + 1, ca + a[i], cb + b[i]] = Math.Min(dp[i + 1, ca + a[i], cb + b[i]], dp[i, ca, cb] + c[i]);
                }
            }
        }

        var val = int.MaxValue;
        for (int ca = 1; ca < n * max; ca++)
        {
            for (int cb = 1; cb < n * max; cb++)
            {
                if (ca * mb == cb * ma)
                {
                    val = Math.Min(val, dp[n, ca, cb]);
                }
            }
        }

        CWL(val == int.MaxValue ? -1 : val);
    }
}

public static partial class Program
{
    //テンプレここから
    public static int ToInt(this string str) => int.Parse(str);
    public static long ToLong(this string str) => long.Parse(str);
    public static long[] ToLong(this IEnumerable<string> strs) => strs.Select(x => x.ToLong()).ToArray();
    public static int[] ToInt(this IEnumerable<string> strs) => strs.Select(x => x.ToInt()).ToArray();
    public static long[] ArrayLongs(this string str, char opr = ' ') => str.Split(opr).ToLong();
    public static int[] ArrayInts(this string str, char opr = ' ') => str.Split(opr).ToInt();
    public static string CRL() => Console.ReadLine();
    public static void CWL(object obj) => Console.WriteLine(obj);
    public static long Diff(long a, long b) => Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    public static long Sign(this long i) => Math.Sign(i);
    public static bool IsEven(this long i) => i % 2 == 0;
    public static bool IsEven(this int i) => i % 2 == 0;
    public static long[] dx = new long[] {0, -1, 0, 1};
    public static long[] dy = new long[] {-1, 0, 1, 0};
    public static long mod = 1000000007;
    public static string alphabet = "abcdefghijklmnopqrstuvwxyz";
    public static long ToLong(this char c) => c.ToString().ToInt();

    public static long[] Sort(this long[] array)
    {
        var list = array.ToList();
        list.Sort();
        return list.ToArray();
    }

    public static long GCD(long a, long b) => b == 0 ? a : GCD(b, a % b);

    public static long LCM(long a, long b) => a * b / GCD(a, b);
    //テンプレここまで
}