#ifndef LOCAL #define FAST_IO #endif // ============ #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i) #define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i) #define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i) #define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__) #define ALL(x) begin(x), end(x) #define LEN(x) (i32)(x.size()) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using i32 = signed int; using i64 = signed long long; using f64 = double; using f80 = long double; using pi = pair; using pl = pair; template using V = vector; template using VV = V>; template using VVV = V>>; template using VVVV = V>>>; template using PQR = priority_queue, greater>; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } template i32 lob(const V &arr, const T &v) { return (i32)(lower_bound(ALL(arr), v) - arr.begin()); } template i32 upb(const V &arr, const T &v) { return (i32)(upper_bound(ALL(arr), v) - arr.begin()); } template V argsort(const V &arr) { V ret(arr.size()); iota(ALL(ret), 0); sort(ALL(ret), [&](i32 i, i32 j) -> bool { if (arr[i] == arr[j]) { return i < j; } else { return arr[i] < arr[j]; } }); return ret; } #ifdef INT128 using u128 = __uint128_t; using i128 = __int128_t; #endif [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct SetUpIO { SetUpIO() { #ifdef FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr); #endif cout << fixed << setprecision(15); } } set_up_io; void scan(char &x) { cin >> x; } void scan(u32 &x) { cin >> x; } void scan(u64 &x) { cin >> x; } void scan(i32 &x) { cin >> x; } void scan(i64 &x) { cin >> x; } void scan(f64 &x) { cin >> x; } void scan(string &x) { cin >> x; } template void scan(V &x) { for (T &ele : x) { scan(ele); } } void read() {} template void read(Head &head, Tail &...tail) { scan(head); read(tail...); } #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__); #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__); #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__); #define I32(...) \ i32 __VA_ARGS__; \ read(__VA_ARGS__); #define I64(...) \ i64 __VA_ARGS__; \ read(__VA_ARGS__); #define F64(...) \ f64 __VA_ARGS__; \ read(__VA_ARGS__); #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__); #define VEC(type, name, size) \ V name(size); \ read(name); #define VVEC(type, name, size1, size2) \ VV name(size1, V(size2)); \ read(name); // ============ #ifdef DEBUGF #else #define DBG(...) (void)0 #endif void solve() { I32(n, x, y); V w(n), v(n), cs(n), c(n); REP(i, n) { read(w[i], v[i], c[i]); } auto judge = [&](double m) -> bool { REP(i, n) { if (v[i] - m * w[i] >= 0) { return true; } } V dp(x, -1E10); REP(i, n) { i32 cc = c[i], ww = w[i] % x; double vv = v[i] - m * w[i] + y * (w[i] / x); DBG(cc, ww, vv); V ndp = dp; REP(j, x) { i32 pos = j; double g = dp[j]; REP(j, cc) { pos += ww; g += vv; if (pos >= x) { pos -= x; g += y; } chmax(ndp[pos], g); } } dp = ndp; DBG(dp); { i32 pos = 0; double g = 0; REP(j, cc) { pos += ww; g += vv; if (pos >= x) { pos -= x; g += y; } chmax(dp[pos], g); } } DBG(dp); if (*max_element(ALL(dp)) >= 0) { return true; } } return false; }; if (judge(1)) { double ok = 1, ng = 1000, error = 1E-6; while (ng - ok > error) { double mid = sqrt(ok * ng); (judge(mid) ? ok : ng) = mid; error = ok * 1E-6; } cout << ok << '\n'; } else { double ok = 0, ng = 1; while (ng - ok > 1E-6) { double mid = (ok + ng) / 2; (judge(mid) ? ok : ng) = mid; } cout << ok << '\n'; } } int main() { i32 t = 1; // cin >> t; while (t--) { solve(); } }