point intersect(line & l, segment s) {
    double da = fabs(l.dist(s.a)), db = fabs(l.dist(s.b));
    if (da + db < eps) {
        return s.a;
    } else {
        double t = da / (da + db);
        return s.a + (s.b - s.a) * t;
    }
}
result lineIntersectsPolygon(line & l, polygon & P, size_t sz, int k) {
    int n = (sz + k - 1) / k;
    double minDist = numeric_limits<double>::max();
    int minPoint = -1;
    unordered_set<int> points;

    if (n <= 50) {
        point prev = P->get(0);
        for (size_t i = k; i < sz; i += k) {
            point cur = P->get(i);
            segment s = {prev, cur};
            if (lineIntersectsSegment(l, s)) {
	            points.insert(i - k);
    	    } else {
	            double dist = fabs(l.dist(cur));
	            if (minDist > dist) {
                    minDist = dist;
                    minPoint = i;
                }
	        }
            prev = cur;
        }
    } else {
        auto ind = lineIntersectsPolygon(l, P, sz, 2 * k);
        if (ind.points.size() != 0) {
            for (int i : ind.points) {
                point p1 = P->get(i - k);
                point p2 = P->get(i);
                segment s = {p1, p2};
                if (lineIntersectsSegment(l, s)) {
                    points.insert((i - k + sz) % sz);
                } else {
                    points.insert(i);
                }
            }
        } else {
            int i = ind.closest;
            point p1 = P->get(i - 2 * k);
            point p2 = P->get(i - k);
            point p3 = P->get(i);
            point p4 = P->get(i + k);
            point p5 = P->get(i + 2 * k);
            point pts[] = {p1, p2, p3, p4, p5};
            segment segs[] = {{p1, p2}, {p2, p3}, {p3, p4}, {p4, p5}};
            for (int j = 0; j < 4; j++) {
                if (lineIntersectsSegment(l, segs[j])) {
                    points.insert((i + k * (j - 2) + sz) % sz);
                }
            }
            for (int j = 0; j < 5; j++) {
                double dist = fabs(l.dist(pts[j]));
                if (minDist > dist) {
                    minDist = dist;
                    minPoint = (i + k * (j - 2) + sz) % sz;
                }
            }
        }
    }

    return {points, minPoint};
}
bool lineIntersectsSegment(line & l, segment & s) {
  double da = l.dist(s.a), db = l.dist(s.b);
  return !((da > eps && db > eps) || (da < -eps && db < -eps));
}