// An AC a day keeps the doctor away.  #pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#ifdef local
#define safe std::cerr<<__PRETTY_FUNCTION__<<" line "<<__LINE__<<" safe\n"
#define debug(args...) qqbx(#args, args)
#define orange(args...) danb(#args, args)
using std::cerr;
template <typename ...T> void qqbx(const char *s, T ...args) {
    int cnt = sizeof...(T);
    ((cerr << "\e[1;32m(" << s << ") = ("), ..., (cerr << args << (--cnt ? ", " : ")\e[0m\n")));
}
template <typename T> void danb(const char *s, T L, T R) {
    cerr << "\e[1;32m[ " << s << " ] = [ ";
    for (int f = 0; L != R; ++L) cerr << (f++ ? ", " : "") << *L;
    cerr << " ]\e[0m\n";
}
#else
#define safe ((void)0)
#define debug(...) ((void)0)
#define orange(...) ((void)0)
#endif // local
#define all(v) begin(v),end(v)

using namespace std;
using ld = long double;
const ld PI = acos(-1);
const ld eps = 1e-9;

using Point = complex<ld>;

ld cross(Point a, Point b) {
    return imag(conj(a) * b);
}
ld dot(Point a, Point b) {
    return real(conj(a) * b);
}
ld angle_diff(Point a, Point b) {
    bool neg = (cross(a, b) <= 0);
    ld res = arg(b) - arg(a);
    if (neg) {
        if (res > 0)
            res -= PI * 2;
        return res;
    } else {
        if (res < 0)
            res += PI * 2;
        return res;
    }
}

vector<Point> intersect_points(ld R, Point a, Point b) {
    // (o - (a+(b-a)t)) dot (b-a) == 0
    // (o - a) dot (b - a) - norm(b-a) t == 0
    ld d = abs(cross(a, b)) / abs(b-a);
    if (d >= R)
        return {};
    ld s = sqrt(R * R - d * d);
    ld t = dot(-a, b-a) / norm(b-a);
    ld l = t - s / abs(b-a), r = t + s / abs(b-a);
    vector<Point> ans;
    if (0 <= l && l <= 1)
        ans.emplace_back(a + (b-a) * l);
    if (0 <= r && r <= 1)
        ans.emplace_back(a + (b-a) * r);
    return ans;
}
ld intersect_area(ld r, Point a, Point b) {
    if (abs(a) >= r && abs(b) >= r) {
        auto ps = intersect_points(r, a, b);
        if (ps.size() < 2) {
            ld theta = angle_diff(a, b);
            return r * r * theta / 2;
        } else {
            assert (ps.size() == 2);
            Point x = ps[0], y = ps[1];
            return r * r * angle_diff(a, x) / 2 + cross(x, y) / 2 + r * r * angle_diff(y, b) / 2;
        }
    }
    if (abs(a) >= r) {
        auto ps = intersect_points(r, a, b);
        if (ps.size() != 1)
            debug(r, a, b);
        assert (ps.size() == 1);
        Point c = ps[0];
        return r * r * angle_diff(a, c) / 2 + cross(c, b) / 2;
    }
    if (abs(b) >= r) {
        auto ps = intersect_points(r, a, b);
        assert (ps.size() == 1);
        Point c = ps[0];
        return cross(a, c) / 2 + r * r * angle_diff(c, b) / 2;
    }
    // (abs(a) <= r && abs(b) <= r)
    return cross(a, b) / 2;
}

signed main() {
    ios_base::sync_with_stdio(0), cin.tie(0);
    int n, r;
    cin >> n >> r;
    vector<Point> p(n);
    for (int i = 0; i < n; i++) {
        int x, y;
        cin >> x >> y;
        p[i] = { x, y };
    }

    auto calc = [&p, n, r](Point o) {
        ld area = 0;
        for (int i = 0; i < n; i++)
            area += intersect_area(r, p[i] - o, p[(i+1)%n] - o);
        return area;
    };
    Point o = 0;
    for (int i = 0; i < n; i++) o += p[i];
    o /= n;

    ld step = 0;
    for (int i = 0; i < n; i++)
        step = max(step, abs(p[i] - o));
    step *= 2;
    mt19937 rng;

    ld cur_best = calc(o);
    for (int i = 0; i < 10000; i++) {
        ld theta = uniform_real_distribution<ld>(-PI, PI)(rng);
        ld now = calc(o + polar(step, theta));
        if (now > cur_best) {
            cur_best = now;
            o += polar(step, theta);
        }
        step *= 0.9999;
    }
    debug(step, o);
    // Point o = {1000, 1000};
    cout << fixed << setprecision(10);
    cout << cur_best << '\n';
}