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: Accepted)

/*
cat <<EOF >mistaken-paste
*/

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>

#define BIG 2000000007
#define VERYBIG 200000000000007LL

#define MOD 1000000007
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 200
#define M_MAX 400

#ifdef __cplusplus
#include <queue>
#include <stack>
#include <tuple>

using namespace std; // I'm NOT gonna use C++ without compro. shit

typedef priority_queue<ull, vector<ull>, greater<ull> > upque123;
typedef priority_queue<ull, vector<ull> > upque321;
typedef priority_queue<sll, vector<sll>, greater<sll> > spque123;
typedef priority_queue<sll, vector<sll> > spque321;

#endif

typedef struct {
	int32_t a;
	int32_t b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	hwll a;
	hwll b;
} linell;


typedef struct {
	ull s;
	ull t;
	int32_t c;
} struct_a;

typedef struct {
	int32_t from;
	int32_t to;
	sll cost;
} struct_b;



const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};

ull n, m;
ull h, w;
ull k;
ull q;
ull vua, vub, vuc, vud, vue, vuf;
sll vsa, vsb, vsc, vsd, vse, vsf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
size_t slen;
size_t tlen;
char ch, dh;

void swap_adj (ull *a, ull *b) {
	if (*a != *b) {
		ull tmp = *b;
		*b = *a;
		*a = tmp;
	}
	return;
}

ull divide (ull a, ull b) {
	ull x = MOD - 2;
	ull ans = 1;
	while (x) {
		if (x & 1) ans = (ans * b) % MOD;
		b = (b * b) % MOD;
		x /= 2;
	}
	return (a * ans) % MOD;
}

int32_t digits (ull x) {
	int32_t i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

int32_t targetdig (ull x, int32_t index /* 1-indexed */) {
	// static...?
	int32_t posmax = digits(x);
	if (posmax < index) return -1;
	while (posmax > index) {
		posmax--;
		x /= 10;
	}
	return x % 10;
}

int32_t charcomp (const char left, const char right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t pcharcomp (const void *left, const void *right) {
	char lval = *(char*)left;
	char rval = *(char*)right;
	return charcomp(lval, rval);
}

int32_t intcomp (const int32_t left, const int32_t right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t pintcomp (const void *left, const void *right) {
	int lval = *(int*)left;
	int rval = *(int*)right;
	return intcomp(lval, rval);
}

int32_t ullcomp (const ull left, const ull right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t pullcomp (const void *left, const void *right) {
	ull lval = *(ull*)left;
	ull rval = *(ull*)right;
	return ullcomp(lval, rval);
}

int32_t pullrevcomp (const void *left, const void *right) {
	ull lval = *(ull*)left;
	ull rval = *(ull*)right;
	return -ullcomp(lval, rval);
}

int32_t sllcomp (const sll left, const sll right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t psllcomp (const void *left, const void *right) {
	sll lval = *(sll*)left, rval = *(sll*)right;
	return ullcomp(lval, rval);
}

int32_t hwllfraccomp (const hwll left, const hwll right) {
	return ullcomp(left.a * right.b, left.b * right.a);
}

int32_t phwAcomp (const hw *left, const hw *right) {
	return intcomp(left->a, right->a);
}

int32_t phwBcomp (const hw *left, const hw *right) {
	return intcomp(left->b, right->b);
}

int32_t phwABcomp (const hw *left, const hw *right) {
	int32_t x = phwAcomp(left, right);
	if (x) return x;
	return phwBcomp(left, right);
}

int32_t phwllAcomp (const hwll *left, const hwll *right) {
	return sllcomp(left->a, right->a);
}

int32_t phwllBcomp (const hwll *left, const hwll *right) {
	return sllcomp(left->b, right->b);
}

int32_t phwllABcomp (const void *left, const void *right) {
	hwll lval = *(hwll*)left, rval = *(hwll*)right;
	int32_t x = sllcomp(lval.a, rval.a);
	if (x) return x;
	return sllcomp(lval.b, rval.b);
}

int32_t phwllrAcBcomp (const hwll *left, const hwll *right) {
	int32_t x = -phwllAcomp(left, right);
	if (x) return x;
	return phwllBcomp(left, right);
}

int32_t phwllBAcomp (const hwll *left, const hwll *right) {
	int32_t x = phwllBcomp(left, right);
	if (x) return x;
	return phwllAcomp(left, right);
}

int32_t pstrAcomp (const struct_a *left, const struct_a *right) {
	int32_t x;
	if (x = ullcomp(left->t, right->t)) return x;
	if (x = ullcomp(left->s, right->s)) return x;
	if (x = intcomp(left->c, right->c)) return x;
	return 0;
}

int32_t bitlet (char c) {
	return (1 << (c - 'a'));
}

ull ullabs (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sllabs (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll nibutanlobo (bool (*func)(sll arg), sll ok, sll ng) {
	while (sllabs(ok, ng) > 1) {
		sll med = (ok + ng) / 2;
		if (func(med)) {
			ok = med;
		} else {
			ng = med;
		}

		// printf("debug: [%lld %lld)\n", ok, ng);
	}

	if (!func(ok)) return ok * 2 - ng;
	return ok;
}

bool nextrouteint (int32_t arr[], int32_t n) {
	int32_t i = n - 1;
	int32_t j, x;

	while (i > 0 && arr[i - 1] > arr[i]) i--;
	if (i == 0) return false;

	x = n;
	for (j = i; j < n; j++) {
		if (arr[j] < arr[i - 1]) continue;
		if (x == n || arr[x] > arr[j]) x = j;
	}
	arr[i - 1] ^= arr[x];
	arr[x] ^= arr[i - 1];
	arr[i - 1] ^= arr[x];

	qsort(&arr[i], n - i, sizeof(int32_t), pintcomp);
	return true;
}

bool nextrouteull (ull arr[], int32_t n) {
	int32_t i = n - 1;
	int32_t j, x;

	while (i > 0 && arr[i - 1] > arr[i]) i--;
	if (i == 0) return false;

	x = n;
	for (j = i; j < n; j++) {
		if (arr[j] < arr[i - 1]) continue;
		if (x == n || arr[x] > arr[j]) x = j;
	}
	arr[i - 1] ^= arr[x];
	arr[x] ^= arr[i - 1];
	arr[i - 1] ^= arr[x];

	qsort(&arr[i], n - i, sizeof(ull), pintcomp);
	return true;
}

void printUquotient (ull left, ull right) {
	const int32_t digits = 20;

	printf("%llu.", left / right);
	left %= right;
	for (int32_t i = 0; i < digits; i++) {
		left *= 10;
		printf("%1d", left / right);
		left %= right;
	}
	puts("");

	return;
}

void printSquotient (sll left, sll right) {
	if (left * right < 0) putchar('-');
	printUquotient(sllabs(left, 0), sllabs(right, 0));

	return;
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#ifdef __cplusplus

typedef struct {
	int32_t to;
	sll cost;
} edge;
typedef pair<sll, int32_t> P;

std::vector<edge> g[N_MAX];
void dijk_init (ull n, struct_b arr[]) {
	edge x;
	for (int32_t i = 0; i < n; i++) {
		x.to = arr[i].to;
		x.cost = arr[i].cost;
		g[arr[i].from].push_back(x);
	}
}

void dijk_distinit (int s, sll distance[], ull n) {
	for (int32_t i = 0; i < n; i++) {
		distance[i] = BIG;
	}
	distance[s] = 0;
	return;
}

bool dijkstra (int s, sll distance[]) {
	priority_queue<P, std::vector<P>, greater<P> > que; // (最短距離, 頂点番号)
	que.push(P(distance[s], s));

	bool ischanged = false;
	while (!que.empty()) {
		P p = que.top();
		que.pop();

		sll v = p.second;
		if (distance[v] < p.first) continue;

		int32_t maxsize = g[v].size();
		for (int32_t i = 0; i < maxsize; i++) {
			edge e = g[v][i];
			if (distance[e.to] > distance[v] + e.cost) {
				distance[e.to] = distance[v] + e.cost;
				ischanged = true;
				que.push(P(distance[e.to], e.to));
			}
		}
	}

	return ischanged;
}

#endif

sll dist[N_MAX];
struct_b path[M_MAX * 2];

ull a[N_MAX];
// sll a[N_MAX];
// ull a[N_MAX][N_MAX];
ull b[N_MAX];
// sll b[N_MAX];
ull c[N_MAX];
// char c[N_MAX];
// char s[N_MAX + 1];
char s[N_MAX + 1][N_MAX + 1];
// char t[N_MAX + 1];

ull alphabets[26];
// char alphabets[26];

// ull dp[N_MAX + 1];
// ull dp[N_MAX + 1][N_MAX + 1];
// bool dp[N_MAX + 1][N_MAX + 1];
// hwll arr[N_MAX];

// typedef tuple<sll, int32_t, int32_t> P2d;

ull leftall[M_MAX + 1][M_MAX + 1];
ull rightall[M_MAX + 1][M_MAX + 1];

double distance (sll x1, sll y1, sll x2, sll y2) {
	double xdist2, ydist2, origindist, dist;

	xdist2 = (x1 - x2) * (x1 - x2);
	ydist2 = (y1 - y2) * (y1 - y2);
	return sqrt(xdist2 + ydist2);
}

ull solve () {
	sll i, j, ki, l;
	ull result = 0;
	// sll result = 0;
	// double result = 0;
	ull maybe = 0;
	// sll maybe = 0;
	ull sum = 0;
	// sll sum = 0;
	ull item;
	ull *dpcell;
	// qsortの際には"p"ullcompを使う

	// result = VERYBIG;
	// for (i = 0; i < (1 << n); i++) {
	// 	if (bitcount(i) != k) continue;

	// 	maybe = 0;
	// 	ull prev = 0;
	// 	for (j = 0; j < n; j++) {
	// 		bool iswatched = (i & (1 << j));

	// 		if (prev >= a[j]) {
	// 			if (iswatched) {	
	// 				maybe += (prev + 1 - a[j]);
	// 				prev++;
	// 			}
	// 		} else {
	// 			prev = a[j];
	// 		}
	// 		// printf("[%llu][%llu] %llu\n", i, j, maybe);
	// 	}
	// 	// printf("[%llu] %llu\n", i, maybe);
	// 	if (maybe < result) result = maybe;
	// }

	ull leftn = n / 2;
	ull rightn = n - leftn;

	ull leftsum = 0, rightsum = 0;
	for (i = 0; i < leftn; i++) leftsum += a[i];
	for (j = 0; j < rightn; j++) rightsum += a[leftn + j];

	for (i = 0; i <= M_MAX; i++) {
		for (j = 0; j <= M_MAX; j++) {
			leftall[i][j] = rightall[i][j] = BIG;
		}
	}
	leftall[0][0] = rightall[0][0] = 0;

	for (i = 0; i < (1 << leftn); i++) {
		ull asum = 0, bsum = 0, csum = 0;
		for (j = 0; j < leftn; j++) {
			if (i & (1 << j)) {
				asum += a[j];
				bsum += b[j];
				csum += c[j];
			}
		}

		dpcell = &leftall[asum][bsum];
		*dpcell = umin(*dpcell, csum);
	}

	for (i = 0; i < (1 << rightn); i++) {
		ull asum = 0, bsum = 0, csum = 0;
		for (j = 0; j < rightn; j++) {
			if (i & (1 << j)) {
				asum += a[leftn + j];
				bsum += b[leftn + j];
				csum += c[leftn + j];
			}
		}

		dpcell = &rightall[asum][bsum];
		*dpcell = umin(*dpcell, csum);
	}

	result = BIG;
	for (i = 0; i <= leftsum; i++) {

		for (j = 0; j <= rightsum; j++) {
			// if (j % 100 == 0) printf("[%llu %llu]\n", i, j);

			ull asum, bsum;

			asum = i;
			while (asum <= leftsum + rightsum) {
				if (((asum * vub) % vua) || !asum) {
					asum++;
					continue;
				}
				bsum = asum * vub / vua;
				if (asum > M_MAX || bsum > M_MAX) break;
				if (bsum >= j) {

					maybe = leftall[i][j] + rightall[asum - i][bsum - j];
					// printf("[%llu + %llu][%llu + %llu] %llu\n", i, (asum - i), j, (bsum - j), maybe);
					if (maybe < result) result = maybe;
				}

				asum += vua / gcd(vua, vub);
			}
			// printf("[%llu][%lld] %llu\n", i, j, maybe);
		}
	}
	// ull asum = vua;
	// while (asum <= M_MAX) {
	// 	ull bsum = (asum / vua) * vub;

	// 	for (i = 0; i <= asum; i++) {
	// 		for (j = 0; j <= bsum; j++) {
	// 			maybe = leftall[i][j] + rightall[asum - i][bsum - j];
	// 			if (maybe < result) result = maybe;
	// 		}
	// 	}

	// 	asum += vua;
	// }
	if (result == BIG) goto fail;

	printf("%llu\n", result);
	// printf("%.12lf\n", (double)result);
	// puts(s);

	return 0;

	success:
	puts("YES");
	// puts("Yes");
	// printf("%llu\n", result);
	// puts("Alice");
	return 0;

	fail:
	// puts("NO");
	// puts("No");
	// puts("0");
	puts("-1");
	// puts("-1 -1 -1");
	// puts("Eel");
	return 1;
}

int32_t main (void) {
	int32_t i, j;
	int32_t x, y;

	// scanf("%lf%lf", &vda, &vdb);
	// scanf("%lld%lld%lld%lld", &vsa, &vsb, &vsc, &vsd);
	// scanf("%llu%llu", &vua, &vub, &vuc, &vud);
	// scanf("%llu%llu", &h, &w);
	scanf("%llu", &n, &m);
	// scanf("%*llu");
	// scanf("%llu", &k, &m, &n);
	scanf("%llu%llu", &vua, &vub, &vuc, &vud, &vue);
	// scanf("%lld", &vsa, &vsb, &vsc);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%llu", &k);
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu", &a[i]);
	// 	// a[i]--;
	// }
	// for (i = 0; i < m; i++) {
	// 	scanf("%llu", &b[i]);
	// }
	// for (i = 0; i < h; i++) {
	// 	scanf("%s", &s[i]);
	// }
	// for (i = 0; i < m; i++) {
	// 	scanf("%llu", &c[i]);
	// 	scanf("%llu", &arr[i].a);
	// 	scanf("%llu", &arr[i].b);
	// 	// arr[i].a--;
	// 	// arr[i].b--;
	// }
	// for (i = 0; i < n; i++) {
	// 	for (j = 0; j < n; j++) {
	// 		scanf("%llu", &a[i][j]);
	// 	}
	// }
	for (i = 0; i < n; i++) {
		scanf("%llu%llu%llu", &a[i], &b[i], &c[i]);
	}

	// scanf("%llu", &q);
	// for (i = 0; i < q; i++) {
	// 	// scanf("%s%s", s, t);
	// 	// solve();
	// }

	// for (i = 0; i < m; i++) {
	// 	scanf("%llu%llu", &arr[i].a, &arr[i].b);
	// 	arr[i].a--;
	// 	arr[i].b--;
	// }
	// for (i = 0; i < n; i++) {
	// 	for (j = 0; j < m; j++) {
	// 		scanf("%llu", &a[i][j]);
	// 		a[i][j]--;
	// 	}
	// }

	solve();

	// for (i = 0; i < m; i++) {
	// 	scanf("%llu%llu%llu", &vua, &vub, &vuc);
	// 	// scanf("%s%s", s, t);
	// 	// scanf("%f%f%f", &vda, &vdb, &vdc);
	// 	// scanf("%s", s);
	// 	solve();
	// }

	// while (scanf("%llu%llu", &n, &k), n + k) {
	// 	for (i = 0; i < n; i++) {
	// 		scanf("%llu", &a[i]);
	// 	}
	// 	solve();
	// }

	return 0;
}