void reconstruct(int start, int skip, vector<int>& lis) {
    if (start != -1) lis.push_back(S[start]);
    vector<pair<int, int>> followers;
    for (int next = start + 1; next < n; ++next) {
        if ((start == -1 || S[start] < S[next]) && lis3(start) == lis3(next) + 1) {
            followers.push_back(make_pair(S[next], next));
        }
    }
    sort(followers.begin(), followers.end());
    for (int i = 0; i < followers.size(); ++i) {
        int idx = followers[i].second;
        int cnt = count(idx);
        if (cnt < skip) {
            skip -= cnt;
        }
        else {
            reconstruct(idx, skip, lis);
            break;
        }
    }
}