ordered_set dfs(int p, int e) {
    d[p] = w[p] + d[e];
    ordered_set ret;
    for (auto u : adj[p]) {
        if (u != e) {
            auto x = dfs(u, p);
            if (x.size() > ret.size()) {
                swap(x, ret);
            }
            for (auto u : x) {
                ret.insert(u);
            }
        }
    }
    //compute the answer for nope p
    ans[p] = ret.order_of_key({d[p], INF});
    ret.insert({d[p] - a[p], p});
    return move(ret);
}