vector<double> solve(vector2 here, vector2 dir, vector<vector2>& center, vector<double>& radius) {
double n = center.size();
dir = dir.normalize();
vector<double> ret;
double cnt=0;
while (cnt < 100) {
double circle = -1;
double time = INF*0.5;
for (double i = 0; i < n; ++i) {
double cand = hitCircle(here, dir, center[i], radius[i] + 1);
if (cand < time) {
time = cand;
circle = i;
}
}
if (circle == -1) break;
cnt++;
ret.push_back(circle);
vector2 contact = here + dir * time;
dir = reflect(here, dir, center[circle], contact);
here = contact;
}
return ret;
}
vector2 project(const vector2& rhs) const {
vector2 r = rhs.normalize();
return r * r.dot(*this);
}