#include <bits/stdc++.h>
using namespace std;
using ui = unsigned int;
using ull = unsigned long long;
using ll = long long;
#define endl '\n'
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int maxn = 2e5 + 10;
const int mod = 1000000007;
#define inl inline
#define fr(i, a, b) for (int i = a; i <= b; i++)
#define ford(i, a, b) for (int i = a; i >= b; i--)
#define forall(i, a) for (auto &i : a)

/**
   ____         ___ _____
  / ___| _   _ / _ \___ /
  \___ \| | | | | | ||_ \
   ___) | |_| | |_| |__) |
  |____/ \__, |\___/____/
         |___/
*/
istream &operator>>(istream &in, vector<int> &v)
{
    for (auto &i : v)
        in >> i;
    return in;
}
ostream &operator<<(ostream &out, vector<int> &v)
{
    for (auto &i : v)
        out << i << " ";
    return out;
}
bool _output = 0;

#include <bits/stdc++.h>
using namespace std;

typedef double db;
const db EPS = 1e-9;

inline int sign(db a)
{
    return a < -EPS ? -1 : a > EPS;
}

inline int cmp(db a, db b)
{
    return sign(a - b);
}

struct P
{
    db x, y;
    P() {}
    P(db _x, db _y) : x(_x), y(_y) {}
    // 重构加减乘除
    P operator+(P p) { return {x + p.x, y + p.y}; }
    P operator-(P p) { return {x - p.x, y - p.y}; }
    P operator*(db d) { return {x * d, y * d}; }
    P operator/(db d) { return {x / d, y / d}; }

    bool operator<(P p) const
    {
        int c = cmp(x, p.x);
        if (c)
            return c == -1;
        return cmp(y, p.y) == -1;
    }

    bool operator==(P o) const { return cmp(x, o.x) == 0 && cmp(y, o.y) == 0; }

    db dot(P p) { return x * p.x + y * p.y; } // 点积
    db det(P p) { return x * p.y - y * p.x; } // 叉积

    db distTo(P p) { return (*this - p).abs(); }
    db alpha() { return atan2(y, x); }
    void read() { cin >> x >> y; }
    void write() { cout << "(" << x << "," << y << ")" << endl; }
    db abs() { return sqrt(abs2()); }
    db abs2() { return x * x + y * y; }
    P rot90() { return P(-y, x); }
    P unit() { return *this / abs(); }
    int quad() const { return sign(y) == 1 || (sign(y) == 0 && sign(x) >= 0); }
    P rot(db an)
    {
        return {x * cos(an) - y * sin(an), x * sin(an) + y * cos(an)};
    }
};

#define cross(p1, p2, p3) \
    ((p2.x - p1.x) * (p3.y - p1.y) - (p3.x - p1.x) * (p2.y - p1.y))
#define crossOp(p1, p2, p3) sign(cross(p1, p2, p3))

// 直线 p1p2, q1q2 是否恰有一个交点
bool chkLL(P p1, P p2, P q1, P q2)
{
    db a1 = cross(q1, q2, p1), a2 = -cross(q1, q2, p2);
    return sign(a1 + a2) != 0;
}

// 求直线 p1p2, q1q2 的交点
P isLL(P p1, P p2, P q1, P q2)
{
    db a1 = cross(q1, q2, p1), a2 = -cross(q1, q2, p2);
    return (p1 * a2 + p2 * a1) / (a1 + a2);
}

// 判断区间 [l1, r1], [l2, r2] 是否相交
bool intersect(db l1, db r1, db l2, db r2)
{
    if (l1 > r1)
        swap(l1, r1);
    if (l2 > r2)
        swap(l2, r2);
    return !(cmp(r1, l2) == -1 || cmp(r2, l1) == -1);
}

// 线段 p1p2, q1q2 相交
bool isSS(P p1, P p2, P q1, P q2)
{
    return intersect(p1.x, p2.x, q1.x, q2.x) &&
           intersect(p1.y, p2.y, q1.y, q2.y) &&
           crossOp(p1, p2, q1) * crossOp(p1, p2, q2) <= 0 &&
           crossOp(q1, q2, p1) * crossOp(q1, q2, p2) <= 0;
}

// 线段 p1p2, q1q2 严格相交
bool isSS_strict(P p1, P p2, P q1, P q2)
{
    return crossOp(p1, p2, q1) * crossOp(p1, p2, q2) < 0 &&
           crossOp(q1, q2, p1) * crossOp(q1, q2, p2) < 0;
}

// m 在 a 和 b 之间
bool isMiddle(db a, db m, db b)
{
    /*if (a > b) swap(a, b);
    return cmp(a, m) <= 0 && cmp(m, b) <= 0;*/
    return sign(a - m) == 0 || sign(b - m) == 0 || (a < m != b < m);
}

bool isMiddle(P a, P m, P b)
{
    return isMiddle(a.x, m.x, b.x) && isMiddle(a.y, m.y, b.y);
}

// 点 p 在线段 p1p2 上
bool onSeg(P p1, P p2, P q)
{
    return crossOp(p1, p2, q) == 0 && isMiddle(p1, q, p2);
}
// q1q2 和 p1p2 的交点 在 p1p2 上？

// 点 p 严格在 p1p2 上
bool onSeg_strict(P p1, P p2, P q)
{
    return crossOp(p1, p2, q) == 0 &&
           sign((q - p1).dot(p1 - p2)) * sign((q - p2).dot(p1 - p2)) < 0;
}

// 求 q 到 直线p1p2 的投影（垂足） ⚠️ : p1 != p2
P proj(P p1, P p2, P q)
{
    P dir = p2 - p1;
    return p1 + dir * (dir.dot(q - p1) / dir.abs2());
}

// 求 q 以 直线p1p2 为轴的反射
P reflect(P p1, P p2, P q)
{
    return proj(p1, p2, q) * 2 - q;
}

// 求 q 到 线段p1p2 的最小距离
db nearest(P p1, P p2, P q)
{
    if (p1 == p2)
        return p1.distTo(q);
    P h = proj(p1, p2, q);
    if (isMiddle(p1, h, p2))
        return q.distTo(h);
    return min(p1.distTo(q), p2.distTo(q));
}

// 求 线段p1p2 与 线段q1q2 的距离
db disSS(P p1, P p2, P q1, P q2)
{
    if (isSS(p1, p2, q1, q2))
        return 0;
    return min(min(nearest(p1, p2, q1), nearest(p1, p2, q2)),
               min(nearest(q1, q2, p1), nearest(q1, q2, p2)));
}

// 极角排序

// sort(p, p + n, [&](P a, P b)
//      {
//     int qa = a.quad(), qb = b.quad();
//     if (qa != qb)
//         return qa < qb;
//     else
//         return sign(a.det(b)) > 0; });

#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, n) for (int i = a; i < n; i++)
typedef double db;
// 求多边形面积
db area(vector<P> ps)
{
    db ret = 0;
    rep(i, 0, ps.size()) ret += ps[i].det(ps[(i + 1) % ps.size()]);
    return ret / 2;
}
// 点包含
int contain(vector<P> ps, P p)
{ // 2:inside,1:on_seg,0:outside
    int n = ps.size(), ret = 0;
    rep(i, 0, n)
    {
        P u = ps[i], v = ps[(i + 1) % n];
        if (onSeg(u, v, p))
            return 1;
        if (cmp(u.y, v.y) <= 0)
            swap(u, v);
        if (cmp(p.y, u.y) > 0 || cmp(p.y, v.y) <= 0)
            continue;
        ret ^= crossOp(p, u, v) > 0;
    }
    return ret * 2;
}
// 严格凸包
vector<P> convexHull(vector<P> ps)
{
    int n = ps.size();
    if (n <= 1)
        return ps;
    sort(ps.begin(), ps.end());
    vector<P> qs(n * 2);
    int k = 0;
    for (int i = 0; i < n; qs[k++] = ps[i++])
        while (k > 1 && crossOp(qs[k - 2], qs[k - 1], ps[i]) <= 0)
            --k;
    for (int i = n - 2, t = k; i >= 0; qs[k++] = ps[i--])
        while (k > t && crossOp(qs[k - 2], qs[k - 1], ps[i]) <= 0)
            --k;
    qs.resize(k - 1);
    return qs;
}

// 不严格凸包
vector<P> convexHullNonStrict(vector<P> ps)
{
    // caution: need to unique the Ps first
    int n = ps.size();
    if (n <= 1)
        return ps;
    sort(ps.begin(), ps.end());
    vector<P> qs(n * 2);
    int k = 0;
    for (int i = 0; i < n; qs[k++] = ps[i++])
        while (k > 1 && crossOp(qs[k - 2], qs[k - 1], ps[i]) < 0)
            --k;
    for (int i = n - 2, t = k; i >= 0; qs[k++] = ps[i--])
        while (k > t && crossOp(qs[k - 2], qs[k - 1], ps[i]) < 0)
            --k;
    qs.resize(k - 1);
    return qs;
}
// 旋转卡壳
db convexDiameter(vector<P> ps)
{
    int n = ps.size();
    if (n <= 1)
        return 0;
    int is = 0, js = 0;
    rep(k, 1, n) is = ps[k] < ps[is] ? k : is, js = ps[js] < ps[k] ? k : js;
    int i = is, j = js;
    db ret = ps[i].distTo(ps[j]);
    do
    {
        if ((ps[(i + 1) % n] - ps[i]).det(ps[(j + 1) % n] - ps[j]) >= 0)
            (++j) %= n;
        else
            (++i) %= n;
        ret = max(ret, ps[i].distTo(ps[j]));
    } while (i != is || j != js);
    return ret;
}

// 切多边形
vector<P> convexCut(const vector<P> &ps, P q1, P q2)
{
    vector<P> qs;
    int n = ps.size();
    rep(i, 0, n)
    {
        P p1 = ps[i], p2 = ps[(i + 1) % n];
        int d1 = crossOp(q1, q2, p1), d2 = crossOp(q1, q2, p2);
        if (d1 >= 0)
            qs.push_back(p1);
        if (d1 * d2 < 0)
            qs.push_back(isLL(p1, p2, q1, q2));
    }
    return qs;
}

#define rep(i, a, n) for (int i = a; i < n; i++)
const double PI = acos(-1.0);

// 判断两个圆的关系
int type(P o1, db r1, P o2, db r2)
{
    db d = o1.distTo(o2);
    if (cmp(d, r1 + r2) == 1)
        return 4;
    if (cmp(d, r1 + r2) == 0)
        return 3;
    if (cmp(d, abs(r1 - r2)) == 1)
        return 2;
    if (cmp(d, abs(r1 - r2)) == 0)
        return 1;
    return 0;
}
// 圆和线相交
vector<P> isCL(P o, db r, P p1, P p2)
{
    if (cmp(abs((o - p1).det(p2 - p1) / p1.distTo(p2)), r) > 0)
        return {};
    db x = (p1 - o).dot(p2 - p1), y = (p2 - p1).abs2(),
       d = x * x - y * ((p1 - o).abs2() - r * r);
    d = max(d, (db)0.0);
    P m = p1 - (p2 - p1) * (x / y), dr = (p2 - p1) * (sqrt(d) / y);
    return {m - dr, m + dr}; // along dir: p1->p2
}

// 两个圆相交的交点
vector<P> isCC(P o1,
               db r1,
               P o2,
               db r2)
{ // need to check whether two circles are the same
    db d = o1.distTo(o2);
    if (cmp(d, r1 + r2) == 1)
        return {};
    if (cmp(d, abs(r1 - r2)) == -1)
        return {};
    d = min(d, r1 + r2);
    db y = (r1 * r1 + d * d - r2 * r2) / (2 * d), x = sqrt(r1 * r1 - y * y);
    P dr = (o2 - o1).unit();
    P q1 = o1 + dr * y, q2 = dr.rot90() * x;
    return {q1 - q2, q1 + q2}; // along circle 1
}

// 求切线，默认求外公切线，求内公切线的话，r2改成负数，求点到圆的切线,r2改成0
//  extanCC, intanCC : -r2, tanCP : r2 = 0
vector<pair<P, P>> tanCC(P o1, db r1, P o2, db r2)
{
    P d = o2 - o1;
    db dr = r1 - r2, d2 = d.abs2(), h2 = d2 - dr * dr;
    if (sign(d2) == 0 || sign(h2) < 0)
        return {};
    h2 = max((db)0.0, h2);
    vector<pair<P, P>> ret;
    for (db sign : {-1, 1})
    {
        P v = (d * dr + d.rot90() * sqrt(h2) * sign) / d2;
        ret.push_back({o1 + v * r1, o2 + v * r2});
    }
    if (sign(h2) == 0)
        ret.pop_back();
    return ret;
}

db rad(P p1, P p2)
{
    return atan2l(p1.det(p2), p1.dot(p2));
}
// 圆和三角形的面积交
db areaCT(db r, P p1, P p2)
{
    vector<P> is = isCL(P(0, 0), r, p1, p2);
    if (is.empty())
        return r * r * rad(p1, p2) / 2;
    bool b1 = cmp(p1.abs2(), r * r) == 1, b2 = cmp(p2.abs2(), r * r) == 1;
    if (b1 && b2)
    {
        P md = (is[0] + is[1]) / 2;
        if (sign((p1 - md).dot(p2 - md)) <= 0)
            return r * r * (rad(p1, is[0]) + rad(is[1], p2)) / 2 +
                   is[0].det(is[1]) / 2;
        else
            return r * r * rad(p1, p2) / 2;
    }
    if (b1)
        return (r * r * rad(p1, is[0]) + is[0].det(p2)) / 2;
    if (b2)
        return (p1.det(is[1]) + r * r * rad(is[1], p2)) / 2;
    return p1.det(p2) / 2;
}

// 内心
P inCenter(P A, P B, P C)
{
    double a = (B - C).abs(), b = (C - A).abs(), c = (A - B).abs();
    return (A * a + B * b + C * c) / (a + b + c);
}
// 外心
P circumCenter(P a, P b, P c)
{
    P bb = b - a, cc = c - a;
    double db = bb.abs2(), dc = cc.abs2(), d = 2 * bb.det(cc);
    return a - P(bb.y * dc - cc.y * db, cc.x * db - bb.x * dc) / d;
}
// 垂心
P othroCenter(P a, P b, P c)
{
    P ba = b - a, ca = c - a, bc = b - c;
    double Y = ba.y * ca.y * bc.y, A = ca.x * ba.y - ba.x * ca.y,
           x0 = (Y + ca.x * ba.y * b.x - ba.x * ca.y * c.x) / A,
           y0 = -ba.x * (x0 - c.x) / ba.y + ca.y;
    return {x0, y0};
}

// 最小圆覆盖,随机增量法
pair<P, db> min_circle(vector<P> ps)
{
    random_device rd;
    mt19937 rng(rd());
    shuffle(ps.begin(), ps.end(), rng);
    // random_shuffle(ps.begin(), ps.end());
    int n = ps.size();
    P o = ps[0];
    db r = 0;
    rep(i, 1, n) if (o.distTo(ps[i]) > r + EPS)
    {
        o = ps[i], r = 0;
        rep(j, 0, i) if (o.distTo(ps[j]) > r + EPS)
        {
            o = (ps[i] + ps[j]) / 2;
            r = o.distTo(ps[i]);
            rep(k, 0, j) if (o.distTo(ps[k]) > r + EPS)
            {
                o = circumCenter(ps[i], ps[j], ps[k]);
                r = o.distTo(ps[i]);
            }
        }
    }
    return {o, r};
}

db intergal(db x, db y, db r, db L, db R)
{
    return r * r * (R - L) + x * r * (sinl(R) - sinl(L)) +
           y * r * (-cosl(R) + cosl(L));
}

db calc_area_circle(P c, db r, db L, db R)
{
    return intergal(c.x, c.y, r, L, R) / 2;
}

db norm(db x)
{
    while (x < 0)
        x += 2 * PI;
    while (x > 2 * PI)
        x -= 2 * PI;
    return x;
}

// 圆面积并
// const int N = 10010;
// P cs[N];
// db rs[N];

// void work()
// {
//     vector<int> cand = {};
//     rep(i, 0, n)
//     {
//         bool ok = 1;
//         rep(j, 0, n) if (i != j)
//         {
//             if (rs[j] > rs[i] + EPS &&
//                 rs[i] + cs[i].distTo(cs[j]) <= rs[j] + EPS)
//             {
//                 ok = 0;
//                 break;
//             }
//             if (cs[i] == cs[j] && cmp(rs[i], rs[j]) == 0 && j < i)
//             {
//                 ok = 0;
//                 break;
//             }
//         }
//         if (ok)
//             cand.push_back(i);
//     }

//     rep(i, 0, cand.size()) cs[i] = cs[cand[i]], rs[i] = rs[cand[i]];
//     n = cand.size();

//     db area = 0;

//     // work
//     rep(i, 0, n)
//     {
//         vector<pair<db, int>> ev = {{0, 0}, {2 * PI, 0}};

//         int cur = 0;

//         rep(j, 0, n) if (j != i)
//         {
//             auto ret = isCC(cs[i], rs[i], cs[j], rs[j]);
//             if (!ret.empty())
//             {
//                 db l = (ret[0] - cs[i]).alpha();
//                 db r = (ret[1] - cs[i]).alpha();
//                 l = norm(l);
//                 r = norm(r);
//                 ev.push_back({l, 1});
//                 ev.push_back({r, -1});
//                 if (l > r)
//                     ++cur;
//             }
//         }

//         sort(ev.begin(), ev.end());
//         rep(j, 0, ev.size() - 1)
//         {
//             cur += ev[j].second;
//             if (cur == 0)
//             {
//                 area += calc_area_circle(cs[i], rs[i], ev[j].fi, ev[j + 1].fi);
//             }
//         }
//     }
// }

void solve()
{
    int n, q;
    cin >> n >> q;
    vector<P> ps;
    for (int i = 0; i < n; i++)
    {
        int x, y;
        cin >> x >> y;
        ps.push_back({x, y});
    }
    auto cv = convexHull(ps);
    n = cv.size();
    cout << fixed << setprecision(10);
    while (q--)
    {
        P a, b;
        cin >> a.x >> a.y >> b.x >> b.y;
        P c = (a + b) / 2;
        auto r = a.distTo(b) / 2;
        db ans = 0;
        ans += .5 * r * r;
        if (contain(cv, c))
        {
            cout << ans << endl;
            continue;
        }
        db t = 1e18;
        for (int i = 0; i < n; i++)
        {
            auto p1 = cv[i], p2 = cv[(i + 1) % n];
            t = min(t, nearest(p1, p2, c));
        }
        ans += t * t;
        cout << ans << endl;
    }
}
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int _ = 1;
    if (_output)
        cin >> _;
    while (_--)
        solve();
    return 0;
}