/* Problem URL: https://codeforces.com/gym/101845/problem/D */ #include #include #include using namespace std; using namespace __gnu_pbds; template > using ordered_set = tree; #define V vector #define rmin(a, b) a = min(a, b) #define rmax(a, b) a = max(a, b) #define rep(i, lim) for (int i = 0; i < (lim); i++) #define nrep(i, s, lim) for (int i = s; i < (lim); i++) #define repv(i, v) for (auto &i : (v)) #define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; } #define sortv(v) sort(v.begin(), v.end()) #define all(v) (v).begin(), (v).end() using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using ll = long long; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; template auto operator<<(ostream &os, const vector &vec)->ostream& { os << vec[0]; for (size_t i = 1; i < vec.size(); i++) { os << ' ' << vec[i]; } os << '\n'; return os; } template auto operator>>(istream &is, vector &vec)->istream& { for (auto &i : vec) { is >> i; } return is; } template auto operator<<(ostream &os, const vector> &vec)->ostream& { for (auto &i : vec) { os << i[0]; for (size_t j = 1; j < i.size(); j++) { os << ' ' << i[j]; } os << '\n'; } return os; } template auto operator>>(istream &is, vector> &vec)->istream& { for (auto &i : vec) { for (auto &j : i) { is >> j; } } return is; } const int oo = INT32_MAX >> 1; const ll OO = INT64_MAX >> 1; struct pt { ll x, y; pt() = default; pt(ll x, ll y): x(x), y(y) {} friend istream &operator >> (istream &is, pt &a) { is >> a.x >> a.y; return is; } ll operator * (pt b) { return x * b.x + y * b.y; } ll operator ^ (pt b) { return x * b.y - y * b.x; } pt operator - (pt b) { return pt(x - b.x, y - b.y); } }; ll sarea2(pt a, pt b, pt c) { return (b - a) ^ (c - a); } int ccw(pt a, pt b, pt c) { ll r = sarea2(a, b, c); return (r > 0) - (r < 0); } void pre() { } #define TEST 0 void solve() { int n, m; cin >> n >> m; V pol(n); cin >> pol; vl pref(n * 3); nrep(i, 1, n * 3) { pref[i] = pref[i - 1] + sarea2(pt(0, 0), pol[(i - 1) % n], pol[i % n]); } ll ans = 0; while (m--) { int l, r; cin >> l >> r; l--, r--; if (l > r) { swap(l, r); } if ((l + 1) % n == r) { continue; } int l2 = r; int r2 = l + n; ll ar1 = abs(sarea2(pt(0, 0), pol[r], pol[l]) + pref[r] - pref[l]); ll ar2 = abs(pref[r2] - pref[l2] + sarea2(pt(0, 0), pol[r2 % n], pol[l2 % n])); rmax(ans, min(ar1, ar2)); } cout << ans / 2.0 << '\n'; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); pre(); int t; (TEST && cin >> t) || (t = 1); while (t--) { solve(); } }