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 (GCC 5.4.1) (judge verdict: Wrong Answer)

/*

import "core"
import "std/algorithm"
import "procon"

const MAX_N := 41
const MAX_AB := 11
const MAX_C := 4001

n := read_int()
ma := read_int()
mb := read_int()

type Yakuhin {
  a Int
  b Int
  c Int
}

var yakuhins Array[40, Yakuhin]
var dp Array[MAX_AB, Array[MAX_AB, Int]]

fn min(a Int, b Int) Int {
  if (a < b) {
    a
  } else {
    b
  }
}

fn print_dp(a Int, b Int) {
  for i in range(1, a) {
    for j in range(1, b) {
      print(get(get(dp, i), j))
      print(" ")
    }
    println("")
  }
}

fn dp1() {
  for i in range(0, n-1) {
    yakuhin := get(yakuhins, i)
    if (get(get(dp, yakuhin.b), yakuhin.a) > yakuhin.c) {
      set(rget(dp, yakuhin.b), yakuhin.a, yakuhin.c)
    }
  }
  for cura in range(1, MAX_AB-1) {
    for curb in range(1, MAX_AB-1) {
      for preva in range(1, cura) {
        prevb := curb - preva
        ca := get(get(dp, prevb), preva)
        cb := get(get(dp, preva), prevb)
        if (get(get(dp, curb), cura) > ca + cb) {
          set(rget(dp, curb), cura, ca + cb)
        }
      }
    }
  }
}

fn main() {
  for i in range(0, n-1) {
    set(yakuhins, i, init(Yakuhin){read_int(); read_int(); read_int()})
  }
  for a in range(0, MAX_AB-1) {
    for b in range(0, MAX_AB-1) {
      set(rget(dp, b), a, int(INF))
    }
  }

  dp1()

  ans := INF
  for a in range(0, MAX_AB-1) {
    for b in range(0, MAX_AB-1) {
      if (a*mb == b*ma) {
        ans = min(ans, get(get(dp, b), a))
      }
    }
  }
  if (ans == INF) {
    println("-1")
  } else {
    println(ans)
  }
}

main()

*/
#define RELEASE

#include "stdbool.h"
#include "stdint.h"
#include "stdlib.h"
#include "string.h"
#include "inttypes.h"
#include "stdio.h"
#include "math.h"


struct core_string_String {
char* p;
int64_t len;
};
struct core_vec_Vec_core_string_String {
struct core_string_String* data;
bool* isinit;
int64_t cap;
int64_t len;
};
struct Array1024_core_prelude_Char { char data[1024]; };
struct d_Yakuhin {
int64_t a;
int64_t b;
int64_t c;
};
struct Array40_d_Yakuhin { struct d_Yakuhin data[40]; };
struct Array11_core_prelude_Int { int64_t data[11]; };
struct Array11_core_array_Array_11_core_prelude_Int { struct Array11_core_prelude_Int data[11]; };

void* core_pointer_nullGG_();
char* core_pointer_plusexclGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(char* core_pointer_p, int64_t core_pointer_i);
char core_string_getGG_core_prelude_CString_core_prelude_Int(char* core_string_cs, int64_t core_string_i);
char core_string_charGG_core_prelude_Int(int64_t core_string_c);
char* core_pointer_allocGcore_prelude_CharG_core_prelude_Int(int64_t core_pointer_len);
void core_pointer_memcpyGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(char* core_pointer_dest, char* core_pointer_src, int64_t core_pointer_len);
struct core_string_String core_string_stringGG_core_prelude_CString(char* core_string_cs);
char* core_string_to_csGG_core_string_String(struct core_string_String core_string_s);
int64_t core_string_lengthGG_core_string_String(struct core_string_String core_string_s);
char* core_pointer_reallocGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(char* core_pointer_ptr, int64_t core_pointer_len);
void core_string_pushGG_core_string_String_core_prelude_CString(struct core_string_String* core_string_dest, char* core_string_src);
bool core_definitions_is_release_fnGG_();
bool core_definitions_is_debug_fnGG_();
int64_t procon_read_intGG_();
int64_t d_minGG_core_prelude_Int_core_prelude_Int(int64_t d_a, int64_t d_b);
void d_dp1GG_();
void d_mainGG_();


bool core_prelude_true;
bool core_prelude_false;
void* core_pointer_nullGG_() {
void* core_pointer_tmpid1 = ((void*)(0));
return core_pointer_tmpid1;
}
void* core_pointer_null;
float core_math_M_PI;
char* core_pointer_plusexclGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(char* core_pointer_p, int64_t core_pointer_i) {
char* core_pointer_tmpid35 = ((char*)((((int64_t)(core_pointer_p)) + core_pointer_i)));
return core_pointer_tmpid35;
}
char core_string_getGG_core_prelude_CString_core_prelude_Int(char* core_string_cs, int64_t core_string_i) {
char core_string_tmpid36 = (*(core_pointer_plusexclGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(((char*)(core_string_cs)), core_string_i)));
return core_string_tmpid36;
}
char core_string_charGG_core_prelude_Int(int64_t core_string_c) {
char core_string_tmpid39 = ((char)(core_string_c));
return core_string_tmpid39;
}
char* core_pointer_allocGcore_prelude_CharG_core_prelude_Int(int64_t core_pointer_len) {
char* core_pointer_tmpid38 = ((char*)(malloc((sizeof(char) * core_pointer_len))));
return core_pointer_tmpid38;
}
void core_pointer_memcpyGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(char* core_pointer_dest, char* core_pointer_src, int64_t core_pointer_len) {
memcpy(((void*)(core_pointer_dest)), ((void*)(core_pointer_src)), (sizeof(char) * core_pointer_len));
}
struct core_string_String core_string_stringGG_core_prelude_CString(char* core_string_cs) {
int64_t core_string_len = strlen(core_string_cs);
struct core_string_String core_string_s = (struct core_string_String){core_pointer_allocGcore_prelude_CharG_core_prelude_Int((core_string_len + 1)), core_string_len};
core_pointer_memcpyGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(core_string_s.p, ((char*)(core_string_cs)), core_string_len);
(*(core_pointer_plusexclGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(core_string_s.p, core_string_len))) = core_string_charGG_core_prelude_Int(0);
struct core_string_String core_string_tmpid40 = core_string_s;
return core_string_tmpid40;
}
char* core_string_to_csGG_core_string_String(struct core_string_String core_string_s) {
char* core_string_tmpid55 = ((char*)(core_string_s.p));
return core_string_tmpid55;
}
int64_t core_string_lengthGG_core_string_String(struct core_string_String core_string_s) {
int64_t core_string_tmpid42 = core_string_s.len;
return core_string_tmpid42;
}
char* core_pointer_reallocGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(char* core_pointer_ptr, int64_t core_pointer_len) {
char* core_pointer_tmpid43 = ((char*)(realloc(((void*)(core_pointer_ptr)), (sizeof(char) * core_pointer_len))));
return core_pointer_tmpid43;
}
void core_string_pushGG_core_string_String_core_prelude_CString(struct core_string_String* core_string_dest, char* core_string_src) {
int64_t core_string_l = (core_string_lengthGG_core_string_String(*core_string_dest) + strlen(core_string_src));
core_string_dest->p = core_pointer_reallocGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(core_string_dest->p, (core_string_l + 1));
core_pointer_memcpyGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(core_pointer_plusexclGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(core_string_dest->p, core_string_lengthGG_core_string_String(*core_string_dest)), ((char*)(core_string_src)), strlen(core_string_src));
(*(core_pointer_plusexclGcore_prelude_CharG_core_pointer_Ptr_core_prelude_Char_core_prelude_Int(core_string_dest->p, core_string_l))) = core_string_charGG_core_prelude_Int(0);
core_string_dest->len = core_string_l;
}
char core_string_cr;
char core_string_lf;
bool core_definitions_is_windows;
bool core_definitions_is_compiletime;
bool core_definitions_is_runtime;
bool core_definitions_is_jscodegen;
bool core_definitions_is_release_fnGG_() {
bool __floritmp1 = core_prelude_true;
bool __floritmp0 = __floritmp1;
bool core_definitions_tmpid65 = __floritmp0;
return core_definitions_tmpid65;
}
bool core_definitions_is_debug_fnGG_() {
bool __floritmp3 = core_prelude_true;
bool __floritmp2 = __floritmp3;
bool core_definitions_tmpid66 = !(__floritmp2);
return core_definitions_tmpid66;
}
bool core_definitions_is_release;
bool core_definitions_is_debug;
#define procon_INF 999999999
#define procon_MOD 1000000007
int64_t procon_read_intGG_() {
int64_t procon_ret;
scanf("%" PRId64, &procon_ret);
int64_t procon_tmpid80 = procon_ret;
return procon_tmpid80;
}
#define d_MAX_N 41
#define d_MAX_AB 11
#define d_MAX_C 4001
int64_t d_n;
int64_t d_ma;
int64_t d_mb;
struct Array40_d_Yakuhin d_yakuhins;
struct Array11_core_array_Array_11_core_prelude_Int d_dp;
int64_t d_minGG_core_prelude_Int_core_prelude_Int(int64_t d_a, int64_t d_b) {
int64_t __floritmp4;
if ((d_a < d_b)) {
__floritmp4 = d_a;
} else {__floritmp4 = d_b;
}int64_t d_tmpid81 = __floritmp4;
return d_tmpid81;
}
void d_dp1GG_() {
{
int64_t d_i = 0;
while ((d_i <= (d_n - 1))) {
struct d_Yakuhin d_yakuhin = ((d_yakuhins).data[d_i]);
if ((((((d_dp).data[d_yakuhin.b])).data[d_yakuhin.a]) > d_yakuhin.c)) {
((&((&d_dp)->data[d_yakuhin.b])))->data[d_yakuhin.a] = d_yakuhin.c;
} else {};
(d_i += 1);
};

}
;
;
;
{
int64_t d_cura = 1;
while ((d_cura <= (d_MAX_AB - 1))) {
{
int64_t d_curb = 1;
while ((d_curb <= (d_MAX_AB - 1))) {
{
int64_t d_preva = 1;
while ((d_preva <= d_cura)) {
int64_t d_prevb = (d_curb - d_preva);
int64_t d_ca = ((((d_dp).data[d_prevb])).data[d_preva]);
int64_t d_cb = ((((d_dp).data[d_preva])).data[d_prevb]);
if ((((((d_dp).data[d_curb])).data[d_cura]) > (d_ca + d_cb))) {
((&((&d_dp)->data[d_curb])))->data[d_cura] = (d_ca + d_cb);
} else {};
(d_preva += 1);
};

}
;
;
;
;
(d_curb += 1);
};

}
;
;
;
;
(d_cura += 1);
};

}
;
;
;
}
void d_mainGG_() {
{
int64_t d_i = 0;
while ((d_i <= (d_n - 1))) {
(&d_yakuhins)->data[d_i] = (struct d_Yakuhin){procon_read_intGG_(), procon_read_intGG_(), procon_read_intGG_()};
;
(d_i += 1);
};

}
;
;
;
{
int64_t d_a = 0;
while ((d_a <= (d_MAX_AB - 1))) {
{
int64_t d_b = 0;
while ((d_b <= (d_MAX_AB - 1))) {
((&((&d_dp)->data[d_b])))->data[d_a] = procon_INF;
;
(d_b += 1);
};

}
;
;
;
;
(d_a += 1);
};

}
;
;
;
d_dp1GG_();
int64_t d_ans = procon_INF;
{
int64_t d_a = 0;
while ((d_a <= (d_MAX_AB - 1))) {
{
int64_t d_b = 0;
while ((d_b <= (d_MAX_AB - 1))) {
if (((d_a * d_mb) == (d_b * d_ma))) {
d_ans = d_minGG_core_prelude_Int_core_prelude_Int(d_ans, ((((d_dp).data[d_b])).data[d_a]));
} else {};
(d_b += 1);
};

}
;
;
;
;
(d_a += 1);
};

}
;
;
;
if ((d_ans == procon_INF)) {
printf("%s", "-1");
;
;
printf("%s", "\n");
;
;
;
} else {printf("%lld", d_ans);
;
;
printf("%s", "\n");
;
;
;
}}

void flori_main() {
core_prelude_true = 1;
core_prelude_false = 0;
core_pointer_null = core_pointer_nullGG_();
core_math_M_PI = M_PI;
core_string_cr = core_string_charGG_core_prelude_Int(13);
core_string_lf = core_string_charGG_core_prelude_Int(10);
core_definitions_is_windows = 
#ifdef _WIN32
#define is_windows true
#elif _WIN64
#define is_windows true
#else
#define is_windows false
#endif
  is_windows;
core_definitions_is_compiletime = 
#ifdef FLORI_COMPILETIME
#define is_compiletime true
#else
#define is_compiletime false
#endif
  is_compiletime;
core_definitions_is_runtime = !(core_definitions_is_compiletime);
core_definitions_is_jscodegen = 
#ifdef FLORI_JSCODEGEN
#define is_jscodegen true
#else
#define is_jscodegen false
#endif
  is_jscodegen;
core_definitions_is_release = core_definitions_is_release_fnGG_();
core_definitions_is_debug = core_definitions_is_debug_fnGG_();
d_n = procon_read_intGG_();
d_ma = procon_read_intGG_();
d_mb = procon_read_intGG_();
d_mainGG_();
}
int main(int argc, char** argv) { flori_main(); }