#include #include #define rep(i, s, n) for (int i = int(s); i < int(n); i++) #define all(v) (v).begin(), (v).end() using boost::multiprecision::cpp_int; using bigint = cpp_int; template void arg_sort_ll(std::vector>& a) { using Point = std::pair; int n = (int)a.size(); std::vector ps(4, std::vector()); auto idx = [](Point v) -> int { if (v.second >= 0) return (v.first >= 0) ? 0 : 1; else return (v.first >= 0) ? 3 : 2; }; for (auto p : a) { assert(!(p.first == 0 && p.second == 0)); ps[idx(p)].emplace_back(p); } a.clear(); a.reserve(n); for (int j = 0; j < 4; j++) { int i = (3 + j) % 4; std::sort(ps[i].begin(), ps[i].end(), [](Point& p1, Point& p2) -> bool { T flag = p1.first * p2.second - p2.first * p1.second; return flag == 0 ? (p1.first * p1.first + p1.second * p1.second < p2.first * p2.first + p2.second * p2.second) : flag > 0; }); for (auto& p : ps[i]) a.emplace_back(p); } return; } using ld = long double; bigint GCD(bigint a, bigint b) { if (b == 0) return a; else return GCD(b, a % b); } struct rational { rational() : p(0), q(1) {} rational(bigint n) : p(n), q(1) {} rational(bigint n, bigint m) { assert(m != 0); if (m < 0) n = -n, m = -m; bigint g = GCD(n, m); p = n / g; q = m / g; } explicit operator const ld() const { return ld(p) / ld(q); } rational& operator+=(const rational& rhs) { bigint g = GCD(q, rhs.q); bigint np = rhs.q / g * p + q / g * rhs.p; bigint nq = q / g * rhs.q; bigint ng = GCD(np, nq); p = np / ng, q = nq / ng; return *this; } rational& operator-=(const rational& rhs) { (*this) += rational(-rhs.p, rhs.q); return *this; } rational& operator*=(const rational& rhs) { bigint g1 = GCD(q, rhs.p), g2 = GCD(p, rhs.q); bigint np = p / g2 * rhs.p / g1; bigint nq = q / g1 * rhs.q / g2; p = np, q = nq; return *this; } rational& operator/=(const rational& rhs) { (*this) *= rational(rhs.q, rhs.p); return *this; } rational operator+() const { return *this; } rational operator-() const { return rational() - *this; } friend rational operator+(const rational& lhs, const rational& rhs) { return rational(lhs) += rhs; } friend rational operator-(const rational& lhs, const rational& rhs) { return rational(lhs) -= rhs; } friend rational operator*(const rational& lhs, const rational& rhs) { return rational(lhs) *= rhs; } friend rational operator/(const rational& lhs, const rational& rhs) { return rational(lhs) /= rhs; } friend bool operator==(const rational& lhs, const rational& rhs) { return lhs.p == rhs.p && lhs.q == rhs.q; } friend bool operator!=(const rational& lhs, const rational& rhs) { return lhs.p != rhs.p || lhs.q != rhs.q; } friend bool operator<(const rational lhs, const rational rhs) { return less_than(lhs, rhs); } friend bool operator>(const rational lhs, const rational rhs) { return less_than(rhs, lhs); } friend bool operator<=(const rational lhs, const rational rhs) { return lhs == rhs || lhs < rhs; } friend bool operator>=(const rational lhs, const rational rhs) { return lhs == rhs || lhs > rhs; } friend std::ostream& operator<<(std::ostream& os, const rational& r) { return os << r.p << " / " << r.q; } std::pair val() const { return {p, q}; } private: bigint p, q; static bool less_than(rational lhs, rational rhs) { bigint lv = lhs.p * rhs.q; bigint rv = lhs.q * rhs.p; return lv < rv; } }; template bool chmin(T& a, T b) { if (a < b) return false; a = b; return true; } int main() { std::cout << std::fixed << std::setprecision(15); int n; bigint h; std::cin >> n >> h; std::vector> ps(n); std::vector xs; for (auto& [x, y] : ps) { std::cin >> x >> y; xs.emplace_back(x); } std::sort(all(xs)); xs.erase(std::unique(all(xs)), xs.end()); std::vector arg_ord; { std::vector> ret; std::map, int> map; rep(i, 0, n) { auto [x, y] = ps[i]; ret.emplace_back(2 * x, 2 * y - h); map[{2 * x, 2 * y - h}] = i; } arg_sort_ll(ret); for (auto [x, y] : ret) { arg_ord.emplace_back(map[{x, y}]); } } rational ans = rational(100000000000); auto calc_score = [](const std::vector& a) -> rational { if (a[2] == 0) { assert(a[1] == 0 && a[2] == 0); return bigint(0); } return rational(a[0]) - rational(a[1] * a[1]) / rational(4 * a[2]); }; for (auto tx : xs) { std::vector u(3, 0), d(3, 0); for (auto [x, y] : ps) { if (x <= tx) { u[0] += (y - h) * (y - h); u[1] += -2 * x * (y - h); u[2] += x * x; } else { d[0] += y * y; d[1] += -2 * x * y; d[2] += x * x; } } chmin(ans, calc_score(u) + calc_score(d)); for (auto i : arg_ord) { auto [x, y] = ps[i]; if (x <= tx) { u[0] -= (y - h) * (y - h); u[1] -= -2 * x * (y - h); u[2] -= x * x; d[0] += y * y; d[1] += -2 * x * y; d[2] += x * x; } else { d[0] -= y * y; d[1] -= -2 * x * y; d[2] -= x * x; u[0] += (y - h) * (y - h); u[1] += -2 * x * (y - h); u[2] += x * x; } chmin(ans, calc_score(u) + calc_score(d)); } } auto [p, q] = ans.val(); std::cout << ld(p) / ld(q) << '\n'; }