#include using namespace std; #define rep(i, n) for (int i = 0; i < n; i++) #define rep2(i, x, n) for (int i = x; i <= n; i++) #define rep3(i, x, n) for (int i = x; i >= n; i--) #define each(e, v) for (auto &e : v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; const int MOD = 1000000007; // const int MOD = 998244353; using ld = long double; int main() { int T; cin >> T; while (T--) { int N; ld X; cin >> N >> X; vector H(N), A(N); rep(i, N) cin >> H[i]; rep(i, N) cin >> A[i]; rep3(i, N - 1, 1) H[i] -= H[i - 1]; X *= 0.5; ld t = A[0]; rep(i, N) A[i] /= t; ld ans = X; ld S = 0; rep2(i, 1, N - 1) { S += H[i - 1] / A[i - 1]; ld L = 0, R = X / S; rep(_, 100) { ld M = (L + R) / 2; ld D = 0; rep(j, i) { D += H[j] * M / sqrt(A[j] * A[j] + M * M); D -= H[j] * A[i] / A[j]; } (D < 0 ? L : R) = M; } // cout << L << '\n'; ld tmp = A[i] * X; rep(j, i) { tmp += H[j] * sqrt(A[j] * A[j] + L * L); tmp -= A[i] * H[j] * L / A[j]; } chmin(ans, tmp); } cout << ans * t * 2 << '\n'; } }