Cut Length

#include <bits/stdc++.h>
using namespace std;
 
using ll = long long;
using ld = long double;
using db = double;
using str = string;  // yay python!
 
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
 
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
 
#define tcT template <class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
tcT > using PR = pair<T, T>;
 
// pairs
#define mp make_pair
#define f first
#define s second
 
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pb push_back
#define eb emplace_back
#define pf push_front
 
#define lb lower_bound
#define ub upper_bound
tcT > int lwb(V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); }
 
// loops
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define trav(a, x) for (auto &a : x)
 
const int MOD = 1e9 + 7;  // 998244353;
const int MX = 2e5 + 5;
const ll INF = 1e18;  // not too close to LLONG_MAX
const ld PI = acos((ld)-1);
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};  // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
 
// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); }  // # of bits set
constexpr int bits(int x) {  // assert(x >= 0); // make C++11 compatible until
	                         // USACO updates ...
	return x == 0 ? 0 : 31 - __builtin_clz(x);
}  // floor(log2(x))
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
 
ll cdiv(ll a, ll b) {
	return a / b + ((a ^ b) > 0 && a % b);
}  // divide a by b rounded up
ll fdiv(ll a, ll b) {
	return a / b - ((a ^ b) < 0 && a % b);
}  // divide a by b rounded down
 
tcT > bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; }  // set a = min(a,b)
tcT > bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
 
tcTU > T fstTrue(T lo, T hi, U f) {
	hi++;
	assert(lo <= hi);  // assuming f is increasing
	while (lo < hi) {  // find first index such that f is true
		T mid = lo + (hi - lo) / 2;
		f(mid) ? hi = mid : lo = mid + 1;
	}
	return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
	lo--;
	assert(lo <= hi);  // assuming f is decreasing
	while (lo < hi) {  // find first index such that f is true
		T mid = lo + (hi - lo + 1) / 2;
		f(mid) ? lo = mid : hi = mid - 1;
	}
	return lo;
}
tcT > void remDup(vector<T> &v) {  // sort and remove duplicates
	sort(all(v));
	v.erase(unique(all(v)), end(v));
}
tcTU > void erase(T &t, const U &u) {  // don't erase
	auto it = t.find(u);
	assert(it != end(t));
	t.erase(it);
}  // element that doesn't exist from (multi)set
 
// INPUT
#define tcTUU tcT, class... U
tcT > void re(complex<T> &c);
tcTU > void re(pair<T, U> &p);
tcT > void re(V<T> &v);
tcT, size_t SZ > void re(AR<T, SZ> &a);
 
tcT > void re(T &x) { cin >> x; }
void re(db &d) {
	str t;
	re(t);
	d = stod(t);
}
void re(ld &d) {
	str t;
	re(t);
	d = stold(t);
}
tcTUU > void re(T &t, U &...u) {
	re(t);
	re(u...);
}
 
tcT > void re(complex<T> &c) {
	T a, b;
	re(a, b);
	c = {a, b};
}
tcTU > void re(pair<T, U> &p) { re(p.f, p.s); }
tcT > void re(V<T> &x) { trav(a, x) re(a); }
tcT, size_t SZ > void re(AR<T, SZ> &x) { trav(a, x) re(a); }
tcT > void rv(int n, V<T> &x) {
	x.rsz(n);
	re(x);
}
 
// TO_STRING
#define ts to_string
str ts(char c) { return str(1, c); }
str ts(const char *s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
#ifdef LOCAL
	return b ? "true" : "false";
#else
	return ts((int)b);
#endif
}
tcT > str ts(complex<T> c) {
	stringstream ss;
	ss << c;
	return ss.str();
}
str ts(V<bool> v) {
	str res = "{";
	F0R(i, sz(v)) res += char('0' + v[i]);
	res += "}";
	return res;
}
template <size_t SZ> str ts(bitset<SZ> b) {
	str res = "";
	F0R(i, SZ) res += char('0' + b[i]);
	return res;
}
tcTU > str ts(pair<T, U> p);
tcT > str ts(T v) {  // containers with begin(), end()
#ifdef LOCAL
	bool fst = 1;
	str res = "{";
	for (const auto &x : v) {
		if (!fst) res += ", ";
		fst = 0;
		res += ts(x);
	}
	res += "}";
	return res;
#else
	bool fst = 1;
	str res = "";
	for (const auto &x : v) {
		if (!fst) res += " ";
		fst = 0;
		res += ts(x);
	}
	return res;
 
#endif
}
tcTU > str ts(pair<T, U> p) {
#ifdef LOCAL
	return "(" + ts(p.f) + ", " + ts(p.s) + ")";
#else
	return ts(p.f) + " " + ts(p.s);
#endif
}
 
// OUTPUT
tcT > void pr(T x) { cout << ts(x); }
tcTUU > void pr(const T &t, const U &...u) {
	pr(t);
	pr(u...);
}
void ps() { pr("\n"); }  // print w/ spaces
tcTUU > void ps(const T &t, const U &...u) {
	pr(t);
	if (sizeof...(u)) pr(" ");
	ps(u...);
}
 
// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU > void DBG(const T &t, const U &...u) {
	cerr << ts(t);
	if (sizeof...(u)) cerr << ", ";
	DBG(u...);
}
#ifdef LOCAL  // compile with -DLOCAL, chk -> fake assert
#define dbg(...)                                                                       \
	cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#define chk(...)                                                                       \
	if (!(__VA_ARGS__))                                                                \
		cerr << "Line(" << __LINE__ << ") -> function(" << __FUNCTION__                \
		     << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n",                   \
		    exit(0);
#else
#define dbg(...) 0
#define chk(...) 0
#endif
 
void setPrec() { cout << fixed << setprecision(15); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
// FILE I/O
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void setIO(str s = "") {
	unsyncIO();
	setPrec();
	// cin.exceptions(cin.failbit);
	// throws exception when do smth illegal
	// ex. try to read letter into int
	if (sz(s)) setIn(s + ".in"), setOut(s + ".out");  // for USACO
}
 
/**
 * Description: Use in place of \texttt{complex<T>}.
 * Source: http://codeforces.com/blog/entry/22175, KACTL
 * Verification: various
 */
 
using T = ld;
int sgn(T a) { return (a > 0) - (a < 0); }
T sq(T a) { return a * a; }
 
typedef pair<T, T> P;
typedef vector<P> vP;
T norm(const P &p) { return sq(p.f) + sq(p.s); }
T abs(const P &p) { return sqrt(norm(p)); }
T arg(const P &p) { return atan2(p.s, p.f); }
P conj(const P &p) { return P(p.f, -p.s); }
P perp(const P &p) { return P(-p.s, p.f); }
P dir(T ang) { return P(cos(ang), sin(ang)); }
 
P operator-(const P &l) { return P(-l.f, -l.s); }
P operator+(const P &l, const P &r) { return P(l.f + r.f, l.s + r.s); }
P operator-(const P &l, const P &r) { return P(l.f - r.f, l.s - r.s); }
P operator*(const P &l, const T &r) { return P(l.f * r, l.s * r); }
P operator*(const T &l, const P &r) { return r * l; }
P operator/(const P &l, const T &r) { return P(l.f / r, l.s / r); }
P operator*(const P &l, const P &r) {
	return P(l.f * r.f - l.s * r.s, l.s * r.f + l.f * r.s);
}
P operator/(const P &l, const P &r) { return l * conj(r) / norm(r); }
P &operator+=(P &l, const P &r) { return l = l + r; }
P &operator-=(P &l, const P &r) { return l = l - r; }
P &operator*=(P &l, const T &r) { return l = l * r; }
P &operator/=(P &l, const T &r) { return l = l / r; }
P &operator*=(P &l, const P &r) { return l = l * r; }
P &operator/=(P &l, const P &r) { return l = l / r; }
 
P unit(const P &p) { return p / abs(p); }
T dot(const P &a, const P &b) { return a.f * b.f + a.s * b.s; }
T cross(const P &a, const P &b) { return a.f * b.s - a.s * b.f; }
T cross(const P &p, const P &a, const P &b) { return cross(a - p, b - p); }
P reflect(const P &p, const P &a, const P &b) {
	return a + conj((p - a) / (b - a)) * (b - a);
}
P foot(const P &p, const P &a, const P &b) { return (p + reflect(p, a, b)) / (T)2; }
bool onSeg(const P &p, const P &a, const P &b) {
	return cross(a, b, p) == 0 && dot(p - a, p - b) <= 0;
}
 
P lineIsect(P a, P b, P c, P d) {
	T x = cross(a, b, c), y = cross(a, b, d);
	T X = cross(c, d, a), Y = cross(c, d, b);
	return (d * x - c * y) / (x - y);  // interior
}
 
/**
 * Description: centroid (center of mass) of a polygon with
 * constant mass per unit area and SIGNED area
 * Time: O(N)
 * Source: http://codeforces.com/blog/entry/22175, KACTL
 * Verification: kattis polygonarea, VT HSPC 2018 Holiday Stars
 */
 
// #include "../Primitives/Point.h"
 
pair<P, T> cenArea(const vP &v) {
	P cen(0, 0);
	T area = 0;
	F0R(i, sz(v)) {
		int j = (i + 1) % sz(v);
		T a = cross(v[i], v[j]);
		cen += a * (v[i] + v[j]);
		area += a;
	}
	return {cen / area / (T)3, area / 2};
}
 
int n, m;
 
int main() {
	setIO();
	re(n, m);
	vP v(n);
	re(v);  // read polygon
	if (cenArea(v).s < 0) reverse(all(v));
	// polygon should be counter clockwise
	F0R(_, m) {
		P a, b;
		re(a, b);  // two points on the line
		vi side;
		trav(t, v) side.pb(sgn(cross(a, b, t)) >= 0);
		T ans = 0;
		F0R(i, n) {
			int j = (i + 1) % sz(side);
			if (side[i] != side[j]) {
				int sign = sgn(cross(v[i] - v[j], b - a));
				// add or subtract "x-coordinate"
				ans += sign * dot(b - a, lineIsect(a, b, v[i], v[j]));
			}
			if (cross(a, b, v[i]) == 0 && cross(a, b, v[j]) == 0 &&
			    dot(b - a, v[j] - v[i]) > 0)
				ans += dot(b - a, v[j] - v[i]);
			// deal with sides that are collinear with the line
		}
		cout << fixed << setprecision(9) << ans / abs(b - a) << "\n";
	}
}