#include <bits/stdc++.h>
using namespace std;
struct Line {
  complex<double> a, b;
  Line(const complex<double> &a, const complex<double> &b) : a(a), b(b) {
    Rep();
  };
  void Rep() {
    if (a.real() == b.real()) {
      a = complex<double>(a.real(), 0);
      b = complex<double>(b.real(), 1);
      return;
    }
    complex<double> c, d;
    d = complex<double>(1, (b.imag() - a.imag()) / (b.real() - a.real()));
    c = complex<double>(0, b.imag() - b.real() * d.imag());
    d = complex<double>(1, d.imag() + c.imag());
    a = c;
    b = d;
  };
};
complex<double> CrossPoint(const Line &l, const Line &r) {
  complex<double> p, ld = l.b - l.a, rd = r.b - r.a, d3 = l.b - r.a;
  double aa = ld.real() * rd.imag() - ld.imag() * rd.real();
  double bb = ld.real() * d3.imag() - ld.imag() * d3.real();
  if (abs(aa) < 1e-9 && abs(bb) < 1e-9) return complex<double>(1e9, -1e9);
  if (abs(aa) < 1e-9) return complex<double>(1e9, 1e9);
  return r.a + bb / aa * (r.b - r.a);
};
int N, M;
int X[1010], Y[1010];
pair<double, double> cross(signed long long x1, signed long long y1,
                           signed long long x2, signed long long y2,
                           signed long long x3, signed long long y3,
                           signed long long x4, signed long long y4) {
  complex<double> p1(x1, y1);
  complex<double> p2(x2, y2);
  complex<double> p3(x3, y3);
  complex<double> p4(x4, y4);
  Line L1(p1, p2), L2(p3, p4);
  complex<double> c = CrossPoint(L1, L2);
  return {c.real(), c.imag()};
}
signed long long comb(double a) {
  if (a == 0) return 0;
  if (a > 0) return a * 100 + 0.1;
  if (a < 0) return -(-a * 100 + 0.1);
}
double hoge(signed long long sx, signed long long sy, signed long long dx,
            signed long long dy) {
  if (dx < 0 || (dx == 0 && dy < 0)) sx += dx, sy += dy, dx = -dx, dy = -dy;
  pair<double, double> st = {sx, sy};
  pair<double, double> ed = {sx + dx, sy + dy};
  signed long long L = max(abs(dx), abs(dy));
  signed long long mul = 100000000 / L + 2;
  pair<double, double> lst = {sx - dx * mul, sy - dy * mul};
  pair<double, double> rst = {sx + dx * mul, sy + dy * mul};
  vector<pair<pair<double, double>, int> > V;
  int i;
  for (i = 0; i < N; i++) {
    pair<double, double> a = {X[i], Y[i]}, b = {X[i + 1], Y[i + 1]};
    signed long long dx2 = X[i + 1] - X[i], dy2 = Y[i + 1] - Y[i];
    signed long long ad = (X[i] - lst.first) * (rst.second - lst.second) -
                          (Y[i] - lst.second) * (rst.first - lst.first);
    signed long long bd = (X[i + 1] - lst.first) * (rst.second - lst.second) -
                          (Y[i + 1] - lst.second) * (rst.first - lst.first);
    if (dy * dx2 == dx * dy2) {
      if (ad == 0 && bd == 0) {
        auto lef = max(st, min(a, b));
        auto ri = min(ed, max(a, b));
        V.push_back({lef, 0});
        V.push_back({ri, 0});
      }
    } else {
      if (ad > 0 && bd > 0)
        continue;
      else if (ad < 0 && bd < 0)
        continue;
      else if (ad == 0)
        V.push_back({{X[i], Y[i]}, (bd > 0) ? 1 : -1});
      else if (bd == 0)
        V.push_back({{X[i + 1], Y[i + 1]}, (ad > 0) ? -1 : 1});
      else {
        auto c = cross(lst.first, lst.second, rst.first, rst.second, X[i], Y[i],
                       X[i + 1], Y[i + 1]);
        V.push_back({c, (ad > 0) ? -2 : 2});
      }
      assert(ad || bd);
    }
  }
  sort((V.begin()), (V.end()));
  pair<double, double> pre = lst;
  int status = 0;
  double len = 0;
  for (auto &r : V) {
    if (status)
      len += hypot(pre.first - r.first.first, pre.second - r.first.second);
    status += r.second;
    pre = r.first;
  }
  return len;
}
void solve() {
  int i, j, k, l, r, x, y;
  string s;
  cin >> N >> M;
  for (i = 0; i < N; i++) {
    double dx, dy;
    cin >> dx >> dy;
    X[i] = comb(dx);
    Y[i] = comb(dy);
  }
  X[N] = X[0];
  Y[N] = Y[0];
  for (r = 0; r < M; r++) {
    double tx1, ty1, tx2, ty2;
    cin >> tx1 >> ty1 >> tx2 >> ty2;
    (void)printf("%.12lf\n", hoge(comb(tx1), comb(ty1), comb(tx2) - comb(tx1),
                                  comb(ty2) - comb(ty1)) /
                                 100.0);
  }
}
int main(int argc, char **argv) {
  string s;
  int i;
  if (argc == 1) ios::sync_with_stdio(false);
  for (i = 0; i < argc - 1; i++) s += argv[i + 1], s += '\n';
  for (i = 0; i < s.size(); i++) ungetc(s[s.size() - 1 - i], stdin);
  solve();
  return 0;
}
