#include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #else #define dbg(x) (x) #endif template struct P { static T_P EPS; static void set_eps(T_P e) { EPS = e; } T_P x, y; P() : x(0), y(0) {} P(T_P x, T_P y) : x(x), y(y) {} P(std::pair p) : x(p.first), y(p.second) {} P operator+(const P &p) const noexcept { return P(x + p.x, y + p.y); } P operator-(const P &p) const noexcept { return P(x - p.x, y - p.y); } P operator*(const P &p) const noexcept { return P(x * p.x - y * p.y, x * p.y + y * p.x); } P operator*(T_P d) const noexcept { return P(x * d, y * d); } P operator/(T_P d) const noexcept { return P(x / d, y / d); } P inv() const { return conj() / norm2(); } P operator/(const P &p) const { return (*this) * p.inv(); } bool operator<(const P &r) const noexcept { return x != r.x ? x < r.x : y < r.y; } bool operator==(const P &r) const noexcept { return x == r.x and y == r.y; } bool operator!=(const P &r) const noexcept { return !((*this) == r); } T_P dot(P p) const noexcept { return x * p.x + y * p.y; } T_P det(P p) const noexcept { return x * p.y - y * p.x; } T_P norm() const noexcept { return std::sqrt(x * x + y * y); } T_P norm2() const noexcept { return x * x + y * y; } T_P arg() const noexcept { return std::atan2(y, x); } // rotate point/vector by rad P rotate(T_P rad) noexcept { return P(x * std::cos(rad) - y * std::sin(rad), x * std::sin(rad) + y * std::cos(rad)); } P normalized() const { return (*this) / this->norm(); } P conj() const noexcept { return P(x, -y); } friend std::istream &operator>>(std::istream &is, P &p) { T_P x, y; is >> x >> y; p = P(x, y); return is; } friend std::ostream &operator<<(std::ostream &os, const P &p) { os << '(' << p.x << ',' << p.y << ')'; return os; } }; template <> double P::EPS = 1e-9; using Float = double; using Pt = P; int N; Float W; vector X; vector R, V, A; Float ret; vector eaten; Pt where(int i, Float sec) { return X[i] + Pt(1, 0).rotate((V[i] * sec + A[i]) / 180. * acos(-1)) * R[i]; } Float sec(Pt pos, Float now, int i) { Float lo = now, hi = now + 1000; REP(_, 50) { Float ss = (lo + hi) / 2; if (lo * hi >= 1) ss = sqrt(lo * hi); Pt tmp = where(i, ss); if ((pos - tmp).norm2() <= W * W * (ss - now) * (ss - now)) hi = ss; else lo = ss; } return hi; } int main() { cin >> N >> W; ret = 1e18; eaten.resize(N); X.resize(N); R.resize(N); V.resize(N); A.resize(N); REP(i, N) cin >> X[i] >> R[i] >> V[i] >> A[i]; vector> dp(N, vector(1 << N, 1e30)); REP(i, N) dp[i][1 << i] = sec({0, 0}, 0, i); REP(S, 1 << N) { REP(j, N) if ((S >> j) & 1) { REP(i, N) if (((S >> i) & 1) == 0) { chmin(dp[i][S + (1 << i)], sec(where(j, dp[j][S]), dp[j][S], i)); } } } if (N <= 3) dbg(dp); for (auto v : dp) chmin(ret, v.back()); cout << ret << '\n'; }