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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdalign>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#endif
#define y0 qvya13579
#define y1 qvyb24680
#define j0 qvja13579
#define j1 qvjb24680
#define next qvne13579xt
#define prev qvpr13579ev
#define INF 1000000007
#define MOD 1000000007
#define PI acos(-1.0)
#define endl "\n"
#define IOS cin.tie(0);ios::sync_with_stdio(false)
#define M_P make_pair
#define PU_B push_back
#define PU_F push_front
#define PO_B pop_back
#define PO_F pop_front
#define U_B upper_bound
#define L_B lower_bound
#define B_S binary_search
#define PR_Q priority_queue
#define FIR first
#define SEC second
#if __cplusplus < 201103L
#define stoi(argument_string) atoi((argument_string).c_str())
#endif
#define REP(i,n) for(int i=0;i<(int)(n);++i)
#define REP_R(i,n) for(int i=((int)(n)-1);i>=0;--i)
#define FOR(i,m,n) for(int i=((int)(m));i<(int)(n);++i)
#define FOR_R(i,m,n) for(int i=((int)(m)-1);i>=(int)(n);--i)
#define ALL(v) (v).begin(),(v).end()
#define RALL(v) (v).rbegin(),(v).rend()
#define SIZ(x) ((int)(x).size())
#define COUT(x) cout<<(x)<<endl
#define CIN(x) cin>>(x)
#define CIN2(x,y) cin>>(x)>>(y)
#define CIN3(x,y,z) cin>>(x)>>(y)>>(z)
#define CIN4(x,y,z,w) cin>>(x)>>(y)>>(z)>>(w)
#define SCAND(x) scanf("%d",&(x))
#define SCAND2(x,y) scanf("%d%d",&(x),&(y))
#define SCAND3(x,y,z) scanf("%d%d%d",&(x),&(y),&(z))
#define SCAND4(x,y,z,w) scanf("%d%d%d%d",&(x),&(y),&(z),&(w))
#define SCANLLD(x) scanf("%lld",&(x))
#define SCANLLD2(x,y) scanf("%lld%lld",&(x),&(y))
#define SCANLLD3(x,y,z) scanf("%lld%lld%lld",&(x),&(y),&(z))
#define SCANLLD4(x,y,z,w) scanf("%lld%lld%lld%lld",&(x),&(y),&(z),&(w))
#define PRINTD(x) printf("%d\n",(x))
#define PRINTLLD(x) printf("%lld\n",(x))
typedef long long int lli;
using namespace std;


bool compare_by_2nd(pair<int,int> a, pair<int,int> b)
{
  if( a.second != b.second )
    {
      return a.second < b.second;
    }
  else
    {
      return a.first < b.first;
    }
  
}

int ctoi(char c)
{
  if( c >= '0' and c <= '9' )
    {
      return (int)(c-'0');
    }

  return -1;
}

int alphabet_pos(char c) 
{
  if( c >= 'a' and c <= 'z' )
    {
      return (int)(c-'a');
    }

  return -1;
}


int alphabet_pos_capital(char c)
{
  if( c >= 'A' and c <= 'Z' )
    {
      return (int)(c-'A');
    }

  return -1;
}


vector<string> split(string str, char ch)
{
  int first = 0;
  int last = str.find_first_of(ch);
  
  if(last == string::npos)
    {
      last = SIZ(str);
    }

  vector<string> result;

  while( first < SIZ(str) )
    {
      string Ssubstr(str, first, last - first);
      result.push_back(Ssubstr);
      first = last + 1;
      last = str.find_first_of(ch, first);

      if(last == string::npos)
	{
	  last = SIZ(str);
	}
    }
  
  return result;
}



int gcd( int a , int b ) // assuming a,b >= 1
{
  if( a < b )
    {
      return gcd( b , a );
      
    }

  if( a % b == 0 )
    {
      return b;
      
    }

  return gcd( b , a % b );
  
}

int lcm( int a , int b ) // assuming a,b >= 1
{
  return  a * b / gcd( a , b );
  
}

lli pow_fast( lli x, lli n_power , lli modulus )
{
  
  if( n_power == 0 )
    {
      return 1;
    }
  
  if( n_power % 2 == 0)
    {
      return pow_fast( x * x % modulus , n_power / 2 , modulus );  
    }

  
  return x * pow_fast( x , n_power - 1 , modulus ) % modulus;
}


struct UnionFind //size-based
{
  vector<int> parent, treesize;
  
  UnionFind( int size ) : parent( size ) , treesize( size , 1 ) //constructor
  {
    for( int i = 0 ; i < size ; ++ i )
      {
	parent[i] = i;
      }
  }

  int root( int x )
  {
    if( parent[x] == x )
      {
	return x;
      }
    
    return parent[x] = root(parent[x]);
  }

  void unite( int x, int y )
  {
    x = root(x); 
    y = root(y);
    
    if( x == y )
      {
	return; 
      }

    if( treesize[x] < treesize[y] )
      {
	parent[x] = y;
	treesize[y] += treesize[x];
      }
    else
      {
	parent[y] = x;
	treesize[x] += treesize[y];	
      }
    
  }

  bool sametree( int x, int y )
  {
    return root(x) == root(y);
  }

  int gettreesize( int x )
  {
    return treesize[root(x)];
  }
  
};



/*------------------ the end of the template -----------------------*/

int N,Ma,Mb;
int a[41];
int b[41];
int c[41];



void pat( vector<int>& a0, vector<int>& b0, vector<int>& c0, int n0, vector<pair<int,int> >& v0, vector<int> ind )
{
  if( SIZ(ind) == n0 )
    {
      int cst = 0;
      int val = 0;
	  
      REP(i,n0)
	{
	  
	  if( ind[i] )
	    {
	      cst += c0[i];
	      val += a0[i] * Mb - b0[i] * Ma;
	    }
	  
	}

      v0.push_back(make_pair(val,cst));
      return;
    }

  REP(j,2)
    {
      vector<int> temp = ind;
      temp.push_back(j);
      pat(a0,b0,c0,n0,v0,temp);
    }
}




int main()
{
  IOS; /* making cin faster */
  SCAND3(N,Ma,Mb);
  REP(i,N)
    {
      SCAND3(a[i],b[i],c[i]);
    }

  int n0 = N/2;
  int n1 = N - n0;

  vector<int> a0(n0), b0(n0), c0(n0);
  vector<int> a1(n1), b1(n1), c1(n1);
  
  REP(i,n0)
    {
      a0[i] = a[i];
      b0[i] = b[i];
      c0[i] = c[i];
      
    }

  REP(i,n1)
    {
      a1[i] = a[i+n0];
      b1[i] = b[i+n0];
      c1[i] = c[i+n0];
      
    }

  vector<pair<int,int> > v0, v1;
  vector<int> ind;
  pat(a0,b0,c0,n0,v0,ind);
  pat(a1,b1,c1,n1,v1,ind);

  sort(ALL(v0));
  sort(ALL(v1));

  int mn = INF;

  REP(i,SIZ(v0))
    {
      int val0 = v0[i].first;
      int cost0 = v0[i].second;

      auto it = lower_bound(ALL(v1),make_pair(-val0,cost0));

      if( it != v1.end() and ( cost0 != 0 or it->second != 0 ) )
	{
	  mn = min( mn, cost0 + it->second );
	}
    }

  if( mn == INF )
    {
      PRINTD(-1);
    }
  else
    {
      PRINTD(mn);
    }
  

}