// Enjoy your stay. Code by evima #include #include #include #include #include #include #include #include #include #include #include #include using namespace atcoder; using mint = modint998244353;// modint1000000007;// modint; #include using namespace std; using ld = long double; using ll = long long; using lll = __int128; using vl = vector; using vs = vector; using LOOPVAR_TYPE = ll; #define all(x) (x).begin(), (x).end() #define sq(x) ((x) * (x)) #define sz(x) ll((x).size()) #define GET_MACRO(_1, _2, _3, NAME, ...) NAME #define rep1(i, n) rep2(i, 0, n) #define rep2(i, a, b) for(LOOPVAR_TYPE i = LOOPVAR_TYPE(a); i < LOOPVAR_TYPE(b); i++) #define rep(...) GET_MACRO(__VA_ARGS__, rep2, rep1)(__VA_ARGS__) #define eb emplace_back #define fir first #define sec second #define mp make_pair #define mt make_tuple const ld EPS = 1e-9; const ld PI = 3.14159265358979323846L; const ll INF = 1070000000LL; const ll MOD = 998244353LL;// 1000000007LL; void fast_io() { cin.tie(NULL); ios_base::sync_with_stdio(false); } ll lin() { ll x; cin >> x; return x; } string input() { string s; cin >> s; return s; } vl vin(int n) { vector v(n); rep(i, n) cin >> v[i]; return v; } template bool chmin(T& a, const T& b) { return (b < a) ? (a = b, true) : false; } template bool chmax(T& a, const T& b) { return (a < b) ? (a = b, true) : false; } template map freq(const vector& v){ map ret; for(T x: v) ++ret[x]; return ret; } template vector reversed(vector v) { reverse(all(v)); return v; } template vector sorted(vector v) { sort(all(v)); return v; } template vector sub(const vector& v, int from, int to) { vector ret; copy(&v[from], &v[to], back_inserter(ret)); return ret; } template string str(const T& x) { stringstream ss; ss << x; return ss.str(); } template array str_tuple_impl(stringstream& ss, Tuple&& t, index_sequence){ return {{ (void( ss << str(get(t)) << " " ), 0)... }}; } template string str_tuple(Tuple&& t){ stringstream ss; str_tuple_impl(ss, forward(t), make_index_sequence>::value>{}); string s = ss.str(); if(s.size() > 0) s.pop_back(); return s; } template string str(const pair& p) { return str_tuple(p); } template string str(const tuple& t) { return str_tuple(t); } template string str(const vector& v) { stringstream ss; rep(i, sz(v)) ss << v[i] << (i < sz(v) - 1 ? " " : ""); return ss.str(); } template void print1(T&& x, const string& end) { cout << str(x) << end; } void print() { print1("", "\n"); } template void print(T&& head, U&&... tail) { print1(head, " "); print(forward(tail)...); } template void eprint1(T&& x, const string& end) { cerr << str(x) << end; } void eprint() { eprint1("", "\n"); } template void eprint(T&& head, U&&... tail) { eprint1(head, " "); eprint(forward(tail)...); } template void quit(T&&... x) { print(forward(x)...); exit(0); } template void yn(bool cnd, T&& yes = "Yes", U&& no = "No") { if(cnd) print(yes); else print(no); } void zip(vl& v) { vl w = v; sort(all(w)); int n = unique(all(w)) - w.begin(); for(ll& x: v) x = lower_bound(&w[0], &w[n], x) - &w[0]; } vl zipped(vl v) { zip(v); return v; } map zipmap(vl v) { map ret; sort(all(v)); v.erase(unique(all(v)), v.end()); rep(i, sz(v)) ret[v[i]] = i; return ret; } const int MN = 12, MX = 100; int N; double W, X[MN + 1], Y[MN + 1], R[MN + 1], V[MN + 1], A[MN + 1]; double dp[1 << MN][MN + 1]; double earliest(int from, int to, double t){ double lo = 0, hi = 6 * MX / W; double sa = (V[from] * t + A[from]) * PI / 180; double sx = X[from] + R[from] * cos(sa); double sy = Y[from] + R[from] * sin(sa); rep(_, 60){ double mi = (lo + hi) / 2; double a = (V[to] * (t + mi) + A[to]) * PI / 180; double tx = X[to] + R[to] * cos(a); double ty = Y[to] + R[to] * sin(a); double dx = tx - sx; double dy = ty - sy; double d = W * mi; (dx * dx + dy * dy < d * d ? hi : lo) = mi; } return t + lo; } void solveOne(){ cin >> N >> W; rep(i, N){ cin >> X[i] >> Y[i] >> R[i] >> V[i] >> A[i]; } rep(mask, 1 << N){ rep(i, N + 1){ dp[mask][i] = mask == 0 && i == N ? 0 : INF; } } rep(mask, (1 << N) - 1){ rep(i, N + 1){ if(mask == 0 && i == N || mask >> i & 1){ rep(j, N){ if(!(mask >> j & 1)){ chmin(dp[mask | 1 << j][j], earliest(i, j, dp[mask][i])); } } } } } cout << *min_element(dp[(1 << N) - 1], dp[(1 << N) - 1] + N + 1) << endl; } int main(){ fast_io(); cout << setprecision(15); int num_tc = 1; // cin >> num_tc; rep(tc, 1, num_tc + 1){ // cout << "Case #" << tc << ": " ;// << endl; solveOne(); } }