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;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;

class Prog
{
    public Prog() { }
    public static int Main()
    {
        new Prog().calc();
        return 0;
    }

    Scanner cin;

    const int max_N = 40;
    const int max_a = 10;
    const int max_c = 100;
    const int INF = 100 * max_c * max_N;

    public void calc()
    {
        cin = new Scanner();
        int N = cin.nextInt();
        int Ma = cin.nextInt();
        int Mb = cin.nextInt();

        int[] a = new int[N];
        int[] b = new int[N];
        int[] c = new int[N];

        for(int i = 0;i<N;i++)
        {
            a[i] = cin.nextInt();
            b[i] = cin.nextInt();
            c[i] = cin.nextInt();
        }

        // dp[i][ca][cb] := 1からi番目までの薬品の組み合わせで,物質Aがcaグラム、物質Bがcbグラムとなる
        //                  溶液の最小のコスト

        int[,,] dp = new int[max_N + 1, (max_a + 1) * max_c + 1, max_a * (max_c + 1) + 1];
        for (int i = 0; i < max_N + 1; i++)
            for (int ca = 0; ca < (max_a + 1) * max_c + 1; ca++)
                for (int cb = 0; cb < max_a * (max_c + 1) + 1; cb++)
                    dp[i, ca, cb] = INF;

        dp[0, 0, 0] = 0;

        for (int i = 0; i < N; i++)
        {
            for (int ca = 0; ca < max_a * max_c; ca++)
            {
                for (int cb = 0; cb < max_a * max_c; cb++)
                {
                    if (dp[i, ca, cb] == INF) continue;
                    dp[i + 1, ca, cb] = Math.Min(dp[i + 1, ca, cb], dp[i, ca, cb]);
                    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]);
                }
            }
        }

        int ans = INF;
        for(int ca = 1;ca< max_a * max_c;ca++)
            for (int cb = 1; cb < max_a * max_c; cb++)
            {
                if (ca * Mb == cb * Ma) ans = Math.Min(ans, dp[N, ca, cb]);
            }

        if (ans == INF) ans = -1;
        Console.WriteLine(ans);
}


    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return s[i++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }
    }
}