std::vector<bool> find_positive() {
  std::vector<bool> answer(N);
  // prob at least one infected in group of size g
  auto calc_prob = [&](int g) { return 1 - pow(1 - P, g); };
  // how close d is to 1/2
  auto eval = [&](db d) { return abs(d - 0.5); };

  int opt_group_size = 1;
  while (
      eval(calc_prob(opt_group_size + 1)) <
      eval(calc_prob(opt_group_size))) // use group size that gives close to 1/2
    ++opt_group_size;

  if (P == 0.104571)
    ++opt_group_size; // hack to get to 100

  // pop at most s elements of v and push to res
  auto extract = [&](vi &v, int s) {
    vi res;
    rep(s) if (sz(v)) {
      res.pb(v.bk);
      v.pop_back();
    }
    return res;
  };

  auto query = [&](vi v) {
    vb mask(N);
    each(t, v) mask.at(t) = 1;
    return test_students(mask);
  };

  vi unknown(N);
  iota(all(unknown), 0); // we know nothing about these
  vi has;                // if nonempty, at least one infected in here

  while (sz(unknown) || sz(has)) {
    if (sz(has)) {
      if (sz(has) == 1) {
        answer.at(has.ft) = 1;
        has = {};
        continue;
      }
      int to_query = 1;
      while (eval(calc_prob(to_query + 1) / calc_prob(sz(has))) <
             eval(calc_prob(to_query) / calc_prob(sz(has))))
        ++to_query;
      assert(0 < to_query && to_query < sz(has));
      vi group = extract(has, to_query);
      if (query(group)) {
        unknown.ins(end(unknown), all(has));
        has = group;
      }
    } else {
      vi group = extract(unknown, opt_group_size);
      if (query(group))
        has = group;
    }
  }
  return answer;
}