#pragma GCC optimize("Ofast") //#pragma GCC target ("sse4") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 998244353; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef long double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acosl(-1.0); ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ld dp[1 << 12][12]; void solve() { int n;ld w; cin >> n >> w; vector x(n), y(n), r(n), v(n), a(n); rep(i, n) { cin >> x[i] >> y[i] >> r[i] >> v[i] >> a[i]; } auto calc = [&](ld cx, ld cy, ld t,int id)->ld { ld dx = abs(cx - x[id]); ld dy = abs(cy - y[id]); ld dist = sqrtl(dx * dx + dy * dy); ld le = (dist - r[id]) / w; if (le < 0)le = 0; ld ri = (dist + r[id]) / w; rep(aa, 80) { ld mid = (le + ri) / 2; ld nx = x[id] + r[id] * cosl((v[id] * (t + mid) + a[id]) * pi / 180.0); ld ny = y[id] + r[id] * sinl((v[id] * (t + mid) + a[id]) * pi / 180.0); ld dx = abs(nx - cx); ld dy = abs(ny - cy); ld dist = sqrtl(dx * dx + dy * dy); if (dist <= w * mid) { ri = mid; } else { le = mid; } } return le; }; rep(i, (1 << n))rep(j, n)dp[i][j] = INF; rep(i, n)dp[(1 << i)][i] = calc(0, 0, 0, i); for (int i = 1; i < (1 << n); i++) { rep(j, n) { if (i & (1 << j)) { ld t = dp[i][j]; ld cx = x[j] + r[j] * cosl((v[j] * t + a[j]) * pi / 180.0); ld cy = y[j] + r[j] * sinl((v[j] * t + a[j]) * pi / 180.0); rep(k, n) { if (k & (1 << i))continue; ld cost = calc(cx, cy, t, k); int ni = i ^ (1 << k); dp[ni][k] = min(dp[ni][k], t + cost); } } } } ld ans = INF; rep(i, n)ans = min(ans, dp[(1 << n) - 1][i]); cout << ans << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(10); //init_f(); //init(); //expr(); //int t; cin >> t; rep(i,t) solve(); return 0; }