#include <bits/stdc++.h>
//#define int long long
#define endl "\n"
using namespace std;

using ll = long long;
const int INF = 1e9;
const int N = 5e3 + 5;
const double eps = 1e-9;

struct Point {
    double x, y;
    using Vec = Point;

    Point operator + (const auto& p) {
        return {x + p.x, y + p.y};
    }

    Point operator - (const auto& p) {
        return {x - p.x, y - p.y};
    }

    Point operator * (const double k) {
        return {x * k, y * k};
    }

    Point operator / (const int k) {
        return {x / k, y / k};
    }

    double cross(const Vec& p) {
        return x * p.y - y * p.x;
    }

    double dis2(const Point& p) {
        return pow(x - p.x, 2) + pow(y - p.y, 2);
    }

    double len2() {
        return pow(x, 2) + pow(y, 2);
    }
} points[N];
using Vec = Point;

double cal(Point& p, Point q) {
    return p.dis2(q);
}

int main() {
    ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);

    int n, q;
    cin >> n >> q;
    for (int i = 1; i <= n; i++) {
        cin >> points[i].x >> points[i].y;
    }
    points[n + 1] = points[1];

    for (int i = 1; i <= q; i++) {
        Point p, q;
        cin >> p.x >> p.y >> q.x >> q.y;
        Point o = (p + q) / 2;
        double r = sqrt(p.dis2(q)) / 2;
        double res = INF;
        bool flag = false;
        for (int j = 1; j <= n; j++) {
            if ((points[j + 1] - points[j]).cross(o - points[j]) <= eps) {
                flag = true;
            }
            double l = 0, r = 1;
            while (r - l > eps) {
                double k = (r - l) / 3;
                double mid1 = l + k, mid2 = r - k;
                if (cal(o, (points[j + 1] - points[j]) * mid1 + points[j]) <= cal(o, (points[j + 1] - points[j]) * mid2 + points[j])) 
                    r = mid2;
                else
                    l = mid1;
            }
            res = min(res, 1.0 * o.dis2((points[j + 1] - points[j]) * l + points[j]));
        }
        if (!flag)
            res = 0;
        res += r * r / 2;
        cout << fixed << setprecision(10) << res << endl;
    }

    return 0;
}