#if __INCLUDE_LEVEL__ == 0

#include <bits/stdc++.h>

using namespace std;

#include __BASE_FILE__

namespace {

void solve() {
  int n, m, q;
  cin >> tie(n, m, q);
  vector<bool> red(n);
  while (m--) {
    int i;
    cin >> i;
    --i;
    red[i] = true;
  }
  HldTree g(n);
  for (int _ = n - 1; _--;) {
    int i, j, w;
    cin >> tie(i, j, w);
    --i, --j;
    g.add_edge({i, j, w});
  }
  g.build(0);
  vector<int64_t> cost(n);
  for (int i : g.order) {
    if (!red[i]) {
      cost[i] = cost[g.pv[i]] + g.edges[g.pe[i]].cost;
    }
  }
  while (q--) {
    int k;
    cin >> k;
    vector<int> vs(k);
    for (int& v : vs) {
      cin >> v;
      --v;
    }
    if (k == 1) {
      print(0);
      continue;
    }
    ranges::sort(vs, {}, [&](int i) { return cost[i]; });
    auto ans = cost[vs.end()[-2]];
    int lca = vs.back();
    int farthest = vs.back();
    for (int t : per(k - 1)) {
      int v = vs[t];
      lca = g.lca(lca, v);
      if (g.distance(lca, farthest) < g.distance(lca, v)) {
        farthest = v;
      }
      chmin(ans, max(t ? cost[vs[t - 1]] : 0, g.distance(lca, farthest)));
    }
    print(ans);
  }
}

}  // namespace

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  int t;
  cin >> t;
  while (t--) {
    solve();
  }
}

#else  // __INCLUDE_LEVEL__

template <class T, class U = T>
bool chmin(T& x, U&& y) {
  return y < x && (x = forward<U>(y), true);
}

template <class T, class U = T>
bool chmax(T& x, U&& y) {
  return x < y && (x = forward<U>(y), true);
}

namespace std {

template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}

template <class... Ts>
istream& operator>>(istream& is, tuple<Ts...>& t) {
  return apply([&is](auto&... xs) -> istream& { return (is >> ... >> xs); }, t);
}

template <class... Ts>
istream& operator>>(istream& is, tuple<Ts&...>&& t) {
  return is >> t;
}

template <class R, enable_if_t<!is_convertible_v<R, string>>* = nullptr>
auto operator>>(istream& is, R&& r) -> decltype(is >> *begin(r)) {
  for (auto&& e : r) {
    is >> e;
  }
  return is;
}

template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << ' ' << p.second;
}

template <class... Ts>
ostream& operator<<(ostream& os, const tuple<Ts...>& t) {
  auto f = [&os](const auto&... xs) -> ostream& {
    [[maybe_unused]] auto sep = "";
    ((os << exchange(sep, " ") << xs), ...);
    return os;
  };
  return apply(f, t);
}

template <class R, enable_if_t<!is_convertible_v<R, string_view>>* = nullptr>
auto operator<<(ostream& os, R&& r) -> decltype(os << *begin(r)) {
  auto sep = "";
  for (auto&& e : r) {
    os << exchange(sep, " ") << e;
  }
  return os;
}

}  // namespace std

template <class... Ts>
void print(Ts&&... xs) {
  cout << tie(xs...) << '\n';
}

inline auto rep(int l, int r) { return views::iota(min(l, r), r); }
inline auto rep(int n) { return rep(0, n); }
inline auto rep1(int l, int r) { return rep(l, r + 1); }
inline auto rep1(int n) { return rep(1, n + 1); }
inline auto per(int l, int r) { return rep(l, r) | views::reverse; }
inline auto per(int n) { return per(0, n); }
inline auto per1(int l, int r) { return per(l, r + 1); }
inline auto per1(int n) { return per(1, n + 1); }

struct Graph {
  struct Edge {
    int src, dst;
    int64_t cost;

    int other(int v) const {
      __glibcxx_assert(v == src or v == dst);
      return src ^ dst ^ v;
    }
  };

  std::vector<Edge> edges;
  std::vector<std::vector<std::pair<int, int>>> adj;

  Graph() {}
  explicit Graph(int n) : adj(n) {}

  int n() const { return std::size(adj); }
  int m() const { return std::size(edges); }
  int add_edge(const Edge& e, bool directed) {
    __glibcxx_assert(0 <= e.src and e.src < n());
    __glibcxx_assert(0 <= e.dst and e.dst < n());
    int id = m();
    edges.push_back(e);
    adj[e.src].emplace_back(e.dst, id);
    if (not directed) adj[e.dst].emplace_back(e.src, id);
    return id;
  }
};

struct DfsTree : Graph {
  using T = decltype(Edge::cost);

  std::vector<int> root;
  std::vector<int> pv;
  std::vector<int> pe;
  std::vector<int> order;
  std::vector<int> in;
  std::vector<int> out;
  std::vector<int> sub;
  std::vector<int> depth;
  std::vector<int> min_depth;
  std::vector<T> dist;
  std::vector<int> last;
  int num_trials;

  DfsTree() {}
  explicit DfsTree(int n)
      : Graph(n),
        root(n, -1),
        pv(n, -1),
        pe(n, -1),
        in(n, -1),
        out(n, -1),
        sub(n, -1),
        depth(n, -1),
        min_depth(n, -1),
        dist(n, std::numeric_limits<T>::max()),
        last(n, -1),
        num_trials(0) {}

  int add_edge(const Edge& e) { return Graph::add_edge(e, false); }
  void dfs(int r, bool clear_order = true) {
    __glibcxx_assert(0 <= r and r < n());
    root[r] = r;
    pv[r] = -1;
    pe[r] = -1;
    if (clear_order) order.clear();
    depth[r] = 0;
    dist[r] = T{};
    dfs_impl(r);
    ++num_trials;
  }
  void dfs_all() {
    std::fill(std::begin(root), std::end(root), -1);
    for (int v = 0; v < n(); ++v)
      if (root[v] == -1) dfs(v, v == 0);
  }

  int deeper(int id) const {
    __glibcxx_assert(0 <= id and id < m());
    int a = edges[id].src;
    int b = edges[id].dst;
    return depth[a] < depth[b] ? b : a;
  }
  bool is_tree_edge(int id) const {
    __glibcxx_assert(0 <= id and id < m());
    return id == pe[deeper(id)];
  }
  bool is_ancestor(int u, int v) const {
    __glibcxx_assert(0 <= u and u < n());
    __glibcxx_assert(0 <= v and v < n());
    return in[u] <= in[v] and out[v] <= out[u];
  }

 private:
  void dfs_impl(int v) {
    in[v] = std::size(order);
    order.push_back(v);
    sub[v] = 1;
    min_depth[v] = depth[v];
    last[v] = num_trials;
    for (auto&& [u, id] : adj[v]) {
      if (id == pe[v]) continue;
      if (last[u] == num_trials) {
        min_depth[v] = std::min(min_depth[v], depth[u]);
        continue;
      }
      root[u] = root[v];
      pv[u] = v;
      pe[u] = id;
      depth[u] = depth[v] + 1;
      dist[u] = dist[v] + edges[id].cost;
      dfs_impl(u);
      sub[v] += sub[u];
      min_depth[v] = std::min(min_depth[v], min_depth[u]);
    }
    out[v] = std::size(order);
  }
};

struct HldTree : DfsTree {
  std::vector<int> head;

  HldTree() {}
  explicit HldTree(int n) : DfsTree(n), head(n, -1) {}

  void build(int r, bool clear_order = true) {
    __glibcxx_assert(0 <= r and r < n());
    dfs(r, clear_order);
    order.erase(std::end(order) - sub[r], std::end(order));
    head[r] = r;
    build_impl(r);
  }
  void build_all() {
    std::fill(std::begin(root), std::end(root), -1);
    for (int v = 0; v < n(); ++v)
      if (root[v] == -1) build(v, v == 0);
  }

  int lca(int u, int v) const {
    __glibcxx_assert(0 <= u and u < n());
    __glibcxx_assert(0 <= v and v < n());
    __glibcxx_assert(root[u] == root[v]);
    while (true) {
      if (in[u] > in[v]) std::swap(u, v);
      if (head[u] == head[v]) return u;
      v = pv[head[v]];
    }
  }
  int d(int u, int v) const {
    __glibcxx_assert(0 <= u and u < n());
    __glibcxx_assert(0 <= v and v < n());
    __glibcxx_assert(root[u] == root[v]);
    return depth[u] + depth[v] - 2 * depth[lca(u, v)];
  }
  T distance(int u, int v) const {
    __glibcxx_assert(0 <= u and u < n());
    __glibcxx_assert(0 <= v and v < n());
    __glibcxx_assert(root[u] == root[v]);
    return dist[u] + dist[v] - 2 * dist[lca(u, v)];
  }
  int la(int v, int d) const {
    __glibcxx_assert(0 <= v and v < n());
    __glibcxx_assert(0 <= d and d <= depth[v]);
    while (depth[head[v]] > d) v = pv[head[v]];
    return order[in[head[v]] + (d - depth[head[v]])];
  }
  int next(int src, int dst) const {
    __glibcxx_assert(0 <= src and src < n());
    __glibcxx_assert(0 <= dst and dst < n());
    __glibcxx_assert(root[src] == root[dst]);
    __glibcxx_assert(src != dst);
    if (not is_ancestor(src, dst)) return pv[src];
    return la(dst, depth[src] + 1);
  }
  int next(int src, int dst, int k) const {
    __glibcxx_assert(0 <= src and src < n());
    __glibcxx_assert(0 <= dst and dst < n());
    __glibcxx_assert(root[src] == root[dst]);
    __glibcxx_assert(k >= 0);
    int v = lca(src, dst);
    if (k <= depth[src] - depth[v]) return la(src, depth[src] - k);
    k -= depth[src] - depth[v];
    __glibcxx_assert(k <= depth[dst] - depth[v]);
    return la(dst, depth[v] + k);
  }
  template <class Function>
  void apply(int src, int dst, bool vertex, Function f) const {
    __glibcxx_assert(0 <= src and src < n());
    __glibcxx_assert(0 <= dst and dst < n());
    __glibcxx_assert(root[src] == root[dst]);
    int v = lca(src, dst);
    while (head[src] != head[v]) {
      f(in[src] + 1, in[head[src]]);
      src = pv[head[src]];
    }
    if (vertex)
      f(in[src] + 1, in[v]);
    else if (src != v)
      f(in[src] + 1, in[v] + 1);
    auto rec = [&](auto self, int to) -> void {
      if (head[v] == head[to]) {
        if (v != to) f(in[v] + 1, in[to] + 1);
        return;
      }
      self(self, pv[head[to]]);
      f(in[head[to]], in[to] + 1);
    };
    rec(rec, dst);
  }
  template <class Searcher>
  int search(int src, int dst, bool vertex, Searcher f) const {
    __glibcxx_assert(0 <= src and src < n());
    __glibcxx_assert(0 <= dst and dst < n());
    __glibcxx_assert(root[src] == root[dst]);
    int res = -1;
    apply(src, dst, vertex, [&](int l, int r) {
      if (res != -1) return;
      int i = f(l, r);
      if (l > r) std::swap(l, r);
      if (l <= i and i < r) res = vertex ? order[i] : pe[order[i]];
    });
    return res;
  }

 private:
  void build_impl(int v) {
    in[v] = std::size(order);
    order.push_back(v);
    auto pos =
        std::partition(std::begin(adj[v]), std::end(adj[v]),
                       [&](auto&& e) { return e.second == pe[e.first]; });
    auto it = std::max_element(
        std::begin(adj[v]), pos,
        [&](auto&& a, auto&& b) { return sub[a.first] < sub[b.first]; });
    if (it != std::begin(adj[v])) std::iter_swap(std::begin(adj[v]), it);
    std::partition(pos, std::end(adj[v]),
                   [&](auto&& e) { return e.second == pe[v]; });
    for (auto&& [u, id] : adj[v]) {
      if (id != pe[u]) break;
      head[u] = u == adj[v].front().first ? head[v] : u;
      build_impl(u);
    }
    out[v] = std::size(order);
  }
};

#endif  // __INCLUDE_LEVEL__