#include <iostream>
#include <cmath>
#include <vector>

using namespace std;

struct point {
    long double x, y;
};

long double dis(point a, point b) {
    long double s;
    s = pow((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y), 0.5);
    return s;
}

long double jiaodu(long double l1, long double l2, long double l3) {
    long double seta;
    seta = acos((l1 * l1 + l2 * l2 - l3 * l3) / (2 * l1 * l2));
    return seta;
}

long double R;

long double operation(point a, point b, point c, point zero) {
    long double r = dis(b, zero);
    long double l1 = dis(a, b);
    long double l2 = dis(b, c);
    long double l3 = dis(a, c);
    long double seta1, seta2, seta3;
    seta1 = jiaodu(l1, l2, l3);
    seta2 = jiaodu(l1, R, R);
    seta3 = jiaodu(l2, R, R);
    return r * (seta2 + seta3 - seta1);
}

int main() {
    int n;
    cin >> n >> R;
    vector<point> v;
    point temp;
    for (int i = 0; i < n; i++) {
        cin >> temp.x >> temp.y;
        v.push_back(temp);
    }
    v.push_back(v[0]);
    v.push_back(v[1]);
    long double sum = 0;
    for (int i = 0; i < n - 1; i++) {
        point a, b, c;
        a = v[i];
        b = v[i + 1];
        c = v[i + 2];
        sum += operation(a, b, c, v[0]);
    }
    printf("%Lf", sum);
    return 0;
}