#include <bits/stdc++.h>
using namespace std;
using db = double;
using vec = complex<db>;
istream& operator >>(istream &in, vec &p) {
	db x, y;
	in >> x >> y;
	p = {x, y};
	return in;
}
#define x real()
#define y imag()
#define C(a, b) (conj(a) * (b)).y
#define D(a, b) (conj(a) * (b)).x
vec foot(vec o, vec p, vec q) {
	return p + (q - p) * (D(q - p, o - p) / norm(q - p));
}
bool onseg(vec h, vec p, vec q) {
	return h.x >= min(p.x, q.x) && h.x <= max(p.x, q.x)
	    && h.y >= min(p.y, q.y) && h.y <= max(p.y, q.y);
}
db dist(vec o, vec p, vec q) {
	vec h = foot(o, p, q);
	if (onseg(h, p, q)) return abs(o - h);
	else return min(abs(o - p), abs(o - q));
}
int main() {
	int n, q;
	cin >> n >> q;
	vector<vec> a(n);
	for (vec &p : a) {
		cin >> p;
	}
	auto inside = [&](vec p) {
		for (int i = 0; i < n; i++) {
			if (C(a[i] - p, a[(i + 1) % n] - p) <= 0) return 0;
		}
		return 1;
	};
	while (q--) {
		vec A, B, O;
		db r;
		cin >> A >> B, O = (A + B) / db(2), r = abs(O - A);
		db d = 1e18;
		if (inside(O)) {
			d = 0;
		} else {
			for (int i = 0; i < n; i++) {
				d = min(d, dist(O, a[i], a[(i + 1) % n]));
			}
		}
		cout << fixed << setprecision(6) << (long double) r * r / 2 + (long double) d * d << "\n";
	}
	return 0;
}