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.IO;
using System.Linq;
using System.Net;
using static System.Console;
using static System.Math;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Security.Cryptography.X509Certificates;
using System.Text.RegularExpressions;
using static CS_Contest.Utils;
using static Nakov.IO.Cin;

//using static CS_Contest.Library;

namespace CS_Contest {
	using Li = List<int>;
	using LLi = List<List<int>>;
	using Ll = List<long>;
	using ti3=Tuple<int,int,int>;
	internal class Program {
		private static void Main(string[] args) {
			var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
			SetOut(sw);
			new Calc().Solve();
			Out.Flush();
		}

		public class Calc {
			public void Solve() {
				int N = NextInt(), Ma = NextInt(), Mb = NextInt();
				var dp = new int[N + 1, 405, 405];//dp
				REP(N + 1, i => REP(405, j => REP(405, k => dp[i, j, k] = int.MaxValue)));
				dp[0, 0, 0] = 0;
				REP(N, i =>
				{
					int ai = NextInt(), bi = NextInt(), ci = NextInt();
					for (int j = 0; j < 405; j++) {
						for (int k = 0; k < 405; k++) {
							if(dp[i,j,k]==int.MaxValue) continue;

							dp[i + 1, j, k] = Min(dp[i, j, k], dp[i + 1, j, k]);
							dp[i + 1, j + ai, k + bi] = Min(dp[i, j, k] + ci, dp[i, j + ai, k + bi]);
						}
					}
				});
				var min = int.MaxValue;

				for (var i = 1; i < 405/Max(Ma,Mb); i++) {
					min = Min(dp[N, i * Ma, i * Mb], min);
				}
				if (min == int.MaxValue) min = -1;
				min.WL();
				return;
			}
		}
	}

	/// <summary>
	/// 優先度付きキュー
	/// </summary>
	/// <typeparam name="T"></typeparam>
	public class PriorityQueue<T> {
		private readonly List<T> heap;
		private readonly Comparison<T> compare;
		private int size;

		public PriorityQueue() : this(Comparer<T>.Default) {
		}

		public PriorityQueue(IComparer<T> comparer) : this(16, comparer.Compare) {
		}

		public PriorityQueue(Comparison<T> comparison) : this(16, comparison) {
		}

		public PriorityQueue(int capacity, Comparison<T> comparison) {
			this.heap = new List<T>(capacity);
			this.compare = comparison;
		}

		public void Enqueue(T item) {
			this.heap.Add(item);
			var i = size++;
			while (i > 0) {
				var p = (i - 1) >> 1;
				if (compare(this.heap[p], item) <= 0)
					break;
				this.heap[i] = heap[p];
				i = p;
			}
			this.heap[i] = item;
		}

		public T Dequeue() {
			var ret = this.heap[0];
			var x = this.heap[--size];
			var i = 0;
			while ((i << 1) + 1 < size) {
				var a = (i << 1) + 1;
				var b = (i << 1) + 2;
				if (b < size && compare(heap[b], heap[a]) < 0) a = b;
				if (compare(heap[a], x) >= 0)
					break;
				heap[i] = heap[a];
				i = a;
			}
			heap[i] = x;
			heap.RemoveAt(size);
			return ret;
		}

		public T Peek() {
			return heap[0];
		}

		public int Count => size;

		public bool Any() {
			return size > 0;
		}
	}

	public class CostGraph
	{
		public struct Edge 
		{
			public int To { get; set; }
			public long Cost { get; set; }


			public Edge(int to, long cost) {
				To = to;
				Cost = cost;
			}

		}

		public int Size { get; set; }
		public List<List<Edge>> Adjacency { get; set; }
		public const long Inf = (long) 1e15;

		public CostGraph(int size) {
			Size = size;
			Adjacency = new List<List<Edge>>();
			REP(Size, _ => Adjacency.Add(new List<Edge>()));
		}

		public void Add(int s, int t, long c, bool dir = true) {
			Adjacency[s].Add(new Edge(t, c));
			if (!dir) Adjacency[t].Add(new Edge(s, c));
		}
	}

	public class Dijkstra : CostGraph
	{
		public Dijkstra(int size) : base(size) {}
		public int[] PreviousNodeList { get; set; }
		public long[] Distance { get; set; }

		public void Run(int s) {
			PreviousNodeList=new int[Size];
			Distance = new long[Size];
			REP(Size, _ => Distance[_] = Inf);

			var pq = new PriorityQueue<Edge>((x, y) => x.Cost.CompareTo(y.Cost));
			Distance[s] = 0;
			pq.Enqueue(new Edge(s, 0));
			while (pq.Any()) {
				var src = pq.Dequeue();
				if(Distance[src.To]<src.Cost) continue;
				for (var i = 0; i < Adjacency[src.To].Count; i++) {
					var tmp = Adjacency[src.To][i];
					var cost = tmp.Cost + src.Cost;
					if(cost>=Distance[tmp.To]) continue;
					Distance[tmp.To] = cost;
					pq.Enqueue(new Edge(tmp.To,cost));
					PreviousNodeList[tmp.To] = src.To;
				}
			}
		}
	}

	public class WarshallFloyd : CostGraph
	{
		public WarshallFloyd(int size) : base(size) {
		}

		public List<Ll> Run() {
			var rt = new List<Ll>();
			REP(Size, _ => rt.Add(new Ll()));

			REP(Size, i => REP(Size, k => rt[i].Add( i == k ? 0 : Inf)));

			ForeachWith(Adjacency, (i, item) =>
			{
				foreach (var k in item) {
					rt[i][k.To] = k.Cost;
				}
			});

			REP(Size, i => REP(Size, j => REP(Size, k =>
			{
				rt[j][k] = Min(rt[j][k], rt[j][i] + rt[i][k]);
			})));

			return rt;
		}
	}

	public static class Utils {

	
		public static void WL(this object obj) => WriteLine(obj);

		public static void WL(this string obj) => WriteLine(obj);


		public static void WL<T>(this IEnumerable<T> list) => list.ToList().ForEach(x => x.WL());

		public static Li ReadInts() => ReadLine().Split().Select(int.Parse).ToList();

		public static string StringJoin<T>(this IEnumerable<T> l, string separator = "") => string.Join(separator, l);

		public static void REP(int n, Action<int> act) {
			for (var i = 0; i < n; i++) {
				act(i);
			}
		}

		public static void ForeachWith<T>(IEnumerable<T> ie, Action<int, T> act) {
			var i = 0;
			foreach (var item in ie) {
				act(i, item);
				i++;
			}
		}


		public static int ManhattanDistance(int x1, int y1, int x2, int y2) => Abs(x2 - x1) + Abs(y2 - y1);

		public struct IndexT<T> {
			public T Value { get; set; }
			public int Index { get; set; }

			public IndexT(T v, int i) {
				Value = v; Index = i;
			}
			public override string ToString() {
				return Value + " " + Index;
			}
		}

		public static IEnumerable<IndexT<T>> ToIndexEnumerable<T>(this IEnumerable<T> list) => list.Select((x, i) => new IndexT<T>(x, i));

		public static Queue<T> ToQueue<T>(this IEnumerable<T> iEnumerable) {
			var rt = new Queue<T>();
			foreach (var item in iEnumerable) {
				rt.Enqueue(item);
			}
			return rt;
		}

		public static IndexT<T> IndexOf<T>(this IEnumerable<T> ie, Func<IndexT<T>, IndexT<T>, IndexT<T>> func) =>
			ie.ToIndexEnumerable().Aggregate(func);

		public static void Swap<T>(ref T x,ref T y) {
			var tmp = x;
			x = y;
			y = tmp;
		}
		public static Dictionary<TKey,int> CountUp<TKey>(this IEnumerable<TKey> l) {
			var dic = new Dictionary<TKey, int>();
			foreach (var item in l) {
				if (dic.ContainsKey(item)) dic[item]++;
				else dic.Add(item, 1);
			}
			return dic;
		}
		public static int Count<T>(this IEnumerable<T> l, T target) => l.Count(x => x.Equals(target));
	}

}
namespace Nakov.IO {
	using System;
	using System.Text;
	using System.Globalization;

	public static class Cin {
		public static string NextToken() {
			StringBuilder tokenChars = new StringBuilder();
			bool tokenFinished = false;
			bool skipWhiteSpaceMode = true;
			while (!tokenFinished) {
				int nextChar = Console.Read();
				if (nextChar == -1) {
					tokenFinished = true;
				} else {
					char ch = (char)nextChar;
					if (char.IsWhiteSpace(ch)) {
						if (!skipWhiteSpaceMode) {
							tokenFinished = true;
							if (ch == '\r' && (Environment.NewLine == "\r\n")) {
								Console.Read();
							}
						}
					} else {
						skipWhiteSpaceMode = false;
						tokenChars.Append(ch);
					}
				}
			}

			string token = tokenChars.ToString();
			return token;
		}

		public static int NextInt() {
			string token = Cin.NextToken();
			return int.Parse(token);
		}
		public static long NextLong() {
			string token = Cin.NextToken();
			return long.Parse(token);
		}
		public static double NextDouble(bool acceptAnyDecimalSeparator = true) {
			string token = Cin.NextToken();
			if (acceptAnyDecimalSeparator) {
				token = token.Replace(',', '.');
				double result = double.Parse(token, CultureInfo.InvariantCulture);
				return result;
			} else {
				double result = double.Parse(token);
				return result;
			}
		}
		public static decimal NextDecimal(bool acceptAnyDecimalSeparator = true) {
			string token = Cin.NextToken();
			if (acceptAnyDecimalSeparator) {
				token = token.Replace(',', '.');
				decimal result = decimal.Parse(token, CultureInfo.InvariantCulture);
				return result;
			} else {
				decimal result = decimal.Parse(token);
				return result;
			}
		}

	}
}