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-csc 3.5.0) (judge verdict: Wrong Answer)

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

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      ABC054.D();
    }
    class ABC054
    {
      public static void A()
      {
        var A = Read.Int();
        var B = Read.Int();
        if (A == 1) { A = 14; }
        if (B == 1) { B = 14; }
        Console.WriteLine(A == B ? "Draw" : A > B ? "Alice" : "Bob");
      }
      public static void B()
      {
        var N = Read.Int();
        var M = Read.Int();
        var A = Enumerable.Range(0, N).Select(i => Read.Str()).ToArray();
        var B = Enumerable.Range(0, M).Select(i => Read.Str()).ToArray();
        for(int i = 0; i <= N - M; ++i)
        {
          for(int j = 0; j <= N - M; ++j)
          {
            bool ok = true;
            for(int k = 0; k < M; ++k)
            {
              for(int l = 0; l < M; ++l)
              {
                if (A[i + k][j + l] != B[k][l])
                {
                  ok = false;
                  break;
                }
              }
              if (!ok) { break; }
            }
            if (ok) { Console.WriteLine("Yes"); return; }
          }
        }
        Console.WriteLine("No");
      }
      public static void C()
      {
        var N = Read.Int();
        var M = Read.Int();
        var Adj = Read.AdjacencyList(N, M);
        var dp = new long[N, 1 << N];
        dp[0, 1] = 1;
        for(int i = 1; i < (1 << N) - 1; ++i)
        {
          for(int j = 0; j < N; ++j)
          {
            if(dp[j, i] == 0) { continue; }
            foreach (var v in Adj[j + 1])
            {
              var k = v - 1;
              if((i & (1 << k)) == 0)
              {
                dp[k, i + (1 << k)] += dp[j, i];
              }
            }
          }
        }
        Console.WriteLine(Enumerable.Range(0, N).Select(x => dp[x, (1 << N) - 1]).Sum());
      }
      public static void D()
      {
        var N = Read.Int();
        var MA = Read.Int();
        var MB = Read.Int();
        var ABC = Enumerable.Range(0, N).Select(i => Read.IntN()).ToArray();
        var dp = Util.Gen(401, 401, Int32.MaxValue);
        dp[0, 0] = 0;
        for(int i = 0; i < N; ++i)
        {
          var A = ABC[i][0];
          var B = ABC[i][1];
          var C = ABC[i][2];
          for (int j = 0; j <= i * 10; ++j)
          {
            for(int k = 0; k <= i * 10; ++k)
            {
              if (dp[j, k] < Int32.MaxValue)
              {
                dp[j + A, k + B] = Math.Min(dp[j + A, k + B], dp[j, k] + C);
              }
            }
          }
        }
        int min = Int32.MaxValue;
        for(int x = 1; ; ++x)
        {
          var A = MA * x;
          var B = MB * x;
          if(A>400 || B > 400) { break; }
          min = Math.Min(min, dp[A, B]);
        }
        Console.WriteLine(min == Int32.MaxValue ? -1 : min);
      }
    }

    class Util
    {
      public static T[,] Gen<T>(int r, int c, T v)
      {
        var matrix = new T[r, c];
        for (int i = 0; i < r; ++i)
        {
          for (int j = 0; j < c; ++j)
          {
            matrix[i, j] = v;
          }
        }
        return matrix;
      }
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static long[,] ASum(long[,] matrix)
      {
        var N = matrix.GetLength(0);
        var M = matrix.GetLength(1);
        var res = new long[N + 1, M + 1];
        for(int i = 0; i < N; ++i)
        {
          for(int j = 0; j < M; ++j)
          {
            res[i + 1, j + 1] = res[i, j + 1] + res[i + 1, j] - res[i, j] + matrix[i, j];
          }
        }
        return res;
      }
      public static Dictionary<T, long> Frequency<T>(T[] array)
      {
        var dict = new Dictionary<T, long>();
        foreach (var a in array)
        {
          if (!dict.ContainsKey(a)) { dict.Add(a, 0); }
          dict[a]++;
        }
        return dict;
      }
      public static long GCD(long a, long b)
      {
        while (b > 0)
        {
          var c = a % b;
          a = b;
          b = c;
        }
        return a;
      }
      public static HashSet<long> Divisor(long x)
      {
        var div = new HashSet<long>(); for (long p = 1; p * p <= x; ++p) { if (x % p == 0) { div.Add(p); } }
        foreach (var d in div.ToArray())
        {
          if (!div.Contains(x / d)) { div.Add(x / d); }
        }
        return div;
      }
      public static Dictionary<long, int> Factorize(long x)
      {
        var dict = new Dictionary<long, int>();
        long minp = 2;
        while (x > 1)
        {
          bool ok = false;
          for (long p = minp; p * p <= x; ++p)
          {
            if (x % p == 0)
            {
              if (!dict.ContainsKey(p))
              {
                dict.Add(p, 0);
              }
              dict[p]++;
              minp = p;
              x /= p;
              ok = true;
              break;
            }
          }
          if (!ok)
          {
            if (!dict.ContainsKey(x)) { dict.Add(x, 0); }
            dict[x]++;
            break;
          }
        }
        return dict;
      }


    }

    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
        for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
        return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); dict[ab[1]].Add(ab[0], ab[2]); }
return dict;
}
}
    }
}