#include<bits/stdc++.h>
using ll = long long;
const int mod = 998244353;
#define double long double

#define pdd std::pair<double, double> 
#define x first
#define y second
const double PI = acos(-1);

std::pair<double, double> operator- (const std::pair<double, double> a, const std::pair<double, double> b) {
    return {a.first - b.first, a.second - b.second};
}

void solve() {
    int n, q;
    std::cin >> n >> q;

    std::vector<std::pair<double, double>> A(n);
    for (int i = 0; i < n; i++) {
        std::cin >> A[i].first >> A[i].second;
    }

    auto dis = [&](pdd a) {
        return sqrt(a.x * a.x + a.y * a.y);
    };
    auto Dot = [&](pdd a, pdd b) {
        return (a.x * b.x + a.y * b.y);
    };
    auto Cro = [&](pdd a, pdd b) {
        return a.x * b.y - a.y * b.x;
    };
    auto cmp = [&](double xx) {
        if (fabs(xx - 1e-8) <= 0.0) return 0.0;
        return (xx < 0.0 ? -1.0 : 1.0);
    };
    auto isCon = [&](double xl, double yl, double xr, double yr) {
        double x = (xl + xr) / 2, y = (yl + yr) / 2;
        pdd o = {x, y};
        std::vector<int> ok(n);
        for (int i = 0; i < n; i++) {
            double x = Cro(A[(i + 1) % n] - A[i], o - A[i]);
            if (cmp(x) == 0) ok[i] = 0;
            if (cmp(x) < 0) ok[i] = -1;
            else ok[i] = 1;
        }
        int mn = *std::min_element(ok.begin(), ok.end());
        int mx = *std::max_element(ok.begin(), ok.end());
        if (mn + mx != 0) return true;
        else return false;
    };
    auto dis_ps = [&](pdd a, pdd b, pdd p) {
        if ((cmp(Dot(p - a, a - b)) >= 0) ^ (cmp(Dot(p - b, a - b)) >= 0)) {
            return fabs(Cro(a - p, b - p)) / dis(a - b);
        }
        else {
            return std::min(dis(p - a), dis(p - b));
        }
    };

    while (q--) {
        double xl, yl, xr, yr;
        std::cin >> xl >> yl >> xr >> yr;
        double ans = dis({xl - xr, yl - yr}) / 2;
        ans = ans * ans / 2.0;
        pdd o = {(xl + xr) / 2, (yl + yr) / 2};
        if (!isCon(xl, yl, xr, yr)) {
            double mn = 1e9;
            for (int i = 0; i < n; i++) {
                mn = std::min(mn, dis_ps(A[i], A[(i + 1) % n], o));
            }
            ans += mn * mn;
        }
        std::cout << std::fixed << std::setprecision(10);
        std::cout << ans << "\n";
    }
}

signed main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int t = 1;
    // std::cin >> t;

    while (t--) {
        solve();
    }
    return 0;
}

answer.code: In function ‘void solve()’:
answer.code:70:30: error: no matching function for call to ‘min(long double&, double)’
   70 |                 mn = std::min(mn, dis_ps(A[i], A[(i + 1) % n], o));
      |                      ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /usr/include/c++/13/algorithm:60,
                 from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:51,
                 from answer.code:1:
/usr/include/c++/13/bits/stl_algobase.h:233:5: note: candidate: ‘template<class _Tp> constexpr const _Tp& std::min(const _Tp&, const _Tp&)’
  233 |     min(const _Tp& __a, const _Tp& __b)
      |     ^~~
/usr/include/c++/13/bits/stl_algobase.h:233:5: note:   template argument deduction/substitution failed:
answer.code:70:30: note:   deduced conflicting types for parameter ‘const _Tp’ (‘long double’ and ‘double’)
   70 |                 mn = std::min(mn, dis_ps(A[i], A[(i + 1) % n], o));
      |                      ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/13/bits/stl_algobase.h:281:5: note: candidate: ‘template<class _Tp, class _Compare> constexpr const _Tp& std::min(const _Tp&, const _Tp&, _Compare)’
  281 |     min(const _Tp& __a, const _Tp& __b, _Compare __comp)
      |     ^~~
/usr/include/c++/13/bits/stl_algobase.h:281:5: note:   template argument deduction/substitution failed:
answer.code:70:30: note:   deduced conflicting types for parameter ‘const _Tp’ (‘long double’ and ‘double’)
   70 |                 mn = std::min(mn, dis_ps(A[i], A[(i + 1) % n], o));
      |                      ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /usr/include/c++/13/algorithm:61:
/usr/include/c++/13/bits/stl_algo.h:5775:5: note: candidate: ‘template<class _Tp> constexpr _Tp std::min(initializer_list<_Tp>)’
 5775 |     min(initializer_list<_Tp> __l)
      |     ^~~
/usr/include/c++/13/bits/stl_algo.h:5775:5: note:   template argument deduction/substitution failed:
answer.code:70:30: note:   mismatched types ‘std::initializer_list<_Tp>’ and ‘long double’
   70 |                 mn = std::min(mn, dis_ps(A[i], A[(i + 1) % n], o));
      |                      ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/13/bits/stl_algo.h:5785:5: note: candidate: ‘template<class _Tp, class _Compare> constexpr _Tp std::min(initializer_list<_Tp>, _Compare)’
 5785 |     min(initializer_list<_Tp> __l, _Compare __comp)
      |     ^~~
/usr/include/c++/13/bits/stl_algo.h:5785:5: note:   template argument deduction/substitution failed:
answer.code:70:30: note:   mismatched types ‘std::initializer_list<_Tp>’ and ‘long double’
   70 |                 mn = std::min(mn, dis_ps(A[i], A[(i + 1) % n], o));
      |                      ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~