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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author gaidash
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DMixingExperiment solver = new DMixingExperiment();
        solver.solve(1, in, out);
        out.close();
    }

    static class DMixingExperiment {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            final int INF = Integer.MAX_VALUE;
            final int MAX = 400;

            int n = in.nextInt();
            int ratioA = in.nextInt();
            int ratioB = in.nextInt();
            DMixingExperiment.Package[] p = new DMixingExperiment.Package[n];
            for (int i = 0; i < n; i++) {
                p[i] = new DMixingExperiment.Package(in.nextInt(), in.nextInt(), in.nextInt());
            }

            int[][][] dp = new int[n + 1][MAX + 1][MAX + 1];
            for (int last = 0; last <= n; last++) {
                for (int a = 0; a <= MAX; a++) {
                    for (int b = 0; b <= MAX; b++) {
                        dp[last][a][b] = INF;
                    }
                }
            }
            dp[0][0][0] = 0;
            for (int last = 1; last <= n; last++) {
                DMixingExperiment.Package cur = p[last - 1];
                for (int a = 0; a <= MAX; a++) {
                    for (int b = 0; b <= MAX; b++) {
                        dp[last][a][b] = Math.min(dp[last][a][b], dp[last - 1][a][b]);
                        if (a - cur.a >= 0 && b - cur.b >= 0 && dp[last - 1][a - cur.a][b - cur.b] != INF) {
                            dp[last][a][b] = Math.min(dp[last][a][b], cur.cost + dp[last - 1][a - cur.a][b - cur.b]);
                        }
                    }
                }
            }

            int ret = INF;
            for (int a = 1; a <= MAX; a++) {
                for (int b = 1; b <= MAX; b++) {
                    if (dp[n][a][b] != INF) {
                        if (a * ratioB == b * ratioA) {
                            ret = Math.min(ret, dp[n][a][b]);
                        }
                    }
                }
            }

            out.println(ret != INF ? ret : -1);
        }

        private static class Package {
            private int a;
            private int b;
            private int cost;

            private Package(int a, int b, int cost) {
                this.a = a;
                this.b = b;
                this.cost = cost;
            }

            public String toString() {
                return "(" + a + " " + b + " " + cost + ")";
            }

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}