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: Wrong Answer)

import java.io.*;
import java.util.*;
import java.math.*;

public class Main {
    public static void main(String[] args) throws Exception {
        PrintWriter out = new PrintWriter(System.out);
        FastScanner fs = new FastScanner();

        n = fs.nextInt(); a = fs.nextInt(); b = fs.nextInt();
        dp = new int[500][500][40];
        for(int i = 0; i < dp.length; i++) {
            for(int j = 0; j < dp[0].length; j++) {
                Arrays.fill(dp[i][j], -1);
            }
        }
        c = new Pack[n];
        for(int i = 0; i < n; i++) c[i] = new Pack(fs.nextInt(), fs.nextInt(), fs.nextInt());
        int res = solve(0, 0, 0, 0);
        if(res == (int)1e9) out.println("-1");
        else out.println(res);

        out.close();
    }

    static class Pack {
        int a, b, c;
        public Pack(int A, int B, int C) {
            a = A; b = B; c = C;
        }
    }

    static int[][][] dp;
    static int n, a, b;
    static Pack[] c;

    static int solve(int at, int cost, int A, int B) {
        if(at == n) {
            double abc = A, bcd = B;
            if(abc / bcd != (double)a/b) {
                return (int)1e9;
            }
            return cost;
        }
        if((double)(A) / (double)B == (double)a / b) {
            return cost;
        }
        if(dp[A][B][at] != -1) return dp[A][B][at];
        int res = (int)1e9;
        //include
        res = Math.min(res, solve(at+1, cost + c[at].c, A + c[at].a, B + c[at].b));
        //exclude
        res = Math.min(res, solve(at+1, cost, A, B));

        return dp[A][B][at] = res;
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            try	{
                br = new BufferedReader(new InputStreamReader(System.in));
                st = new StringTokenizer("");
            } catch (Exception e){e.printStackTrace();}
        }

        public String next() {
            if (st.hasMoreTokens())	return st.nextToken();
            try {st = new StringTokenizer(br.readLine());}
            catch (Exception e) {e.printStackTrace();}
            return st.nextToken();
        }

        public int nextInt() {return Integer.parseInt(next());}

        public long nextLong() {return Long.parseLong(next());}

        public double nextDouble() {return Double.parseDouble(next());}

        public String nextLine() {
            String line = "";
            try {line = br.readLine();}
            catch (Exception e) {e.printStackTrace();}
            return line;
        }

        public Integer[] nextIntegerArray(int n) {
            Integer[] a = new Integer[n];
            for(int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for(int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        public char[] nextCharArray() {
            return nextLine().toCharArray();
        }
    }
}