#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
using namespace std;
using ld = long double;
constexpr ld eps = 1e-8;
using vec = complex<ld>;
using cv = const vec&;
istream& operator >>(istream &in, vec &p) {
	ld 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(cv o, cv p, cv q) {
	return p + (q - p) * (D(q - p, o - p) / norm(q - p));
}
bool onseg(cv h, cv p, cv q) {
	return h.x > min(p.x, q.x) - eps && h.x < max(p.x, q.x) + eps
	    && h.y > min(p.y, q.y) - eps && h.y < max(p.y, q.y) + eps;
}
ld dist(cv o, cv p, cv q) {
	cv 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;
	}
	ld s0 = 0;
	for (int i = 0; i < n; i++) {
		s0 += C(a[i], a[(i + 1) % n]);
	}
	auto inside = [&](cv p) {
		ld s1 = 0;
		for (int i = 0; i < n; i++) {
			s1 += fabs(C(a[i] - p, a[(i + 1) % n] - p));
		}
		return fabs(s0 - s1) < eps;
	};
	while (q--) {
		vec A, B, O;
		ld r;
		cin >> A >> B, O = (A + B) / ld(2), r = abs(O - A);
		ld 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) << r * r / 2 + d * d << "\n";
	}
	return 0;
}