#include <bits/stdc++.h>
#ifdef dbg
#define D(...) fprintf(stderr, __VA_ARGS__)
#define DD(...) D(#__VA_ARGS__ " = "), debug_helper::debug(__VA_ARGS__), D("\n")
#include "C:\Users\wsyear\Desktop\OI\templates\debug.hpp"
#else
#define D(...) ((void)0)
#define DD(...) ((void)0)
#endif
#define rep(i, j, k) for (int i = (j); i <= (k); ++i)
#define per(i, j, k) for (int i = (j); i >= (k); --i)
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;

using namespace std;

const int N = 100010;

int n, m, q, mm, dep[N], rt[N], sum[N], red[N], fa[N][20];
ll len[N][20], val[N], mx[N];
vector<pii> e[N];

void dfs(int u) {
  if (red[u]) val[u] = 0;
  for (auto nxt : e[u]) {
    int v = nxt.fi, w = nxt.se;
    if (v == fa[u][0]) continue;
    fa[v][0] = u, len[v][0] = w;
    dep[v] = dep[u] + 1;
    val[v] = val[u] + w, dfs(v);
  }
}

int lca(int u, int v) {
  if (dep[u] < dep[v]) swap(u, v);
  int dc = dep[u] - dep[v];
  per (i, 19, 0) if (dc >> i & 1) u = fa[u][i];
  if (u == v) return u;
  per (i, 19, 0) if (fa[u][i] != fa[v][i]) u = fa[u][i], v = fa[v][i];
  return fa[u][0];
}

ll LEN(int u, int v) {
  ll res = 0;
  int dc = dep[u] - dep[v];
  per (i, 19, 0) {
    if (dc >> i & 1) {
      res += len[u][i];
      u = fa[u][i];
    }
  }
  return res;
}

void work() {
  cin >> n >> m >> q;
  rep (i, 1, n) {
    red[i] = 0;
    e[i].clear();
  }
  rep (i, 1, m) {
    int x; cin >> x;
    red[x] = 1;
  }
  rep (i, 1, n - 1) {
    int u, v, w;
    cin >> u >> v >> w;
    e[u].emplace_back(v, w);
    e[v].emplace_back(u, w);
  }
  dfs(1);
  rep (j, 1, 19) rep (i, 1, n) {
    fa[i][j] = fa[fa[i][j - 1]][j - 1];
    len[i][j] = len[i][j - 1] + len[fa[i][j - 1]][j - 1];
  }
  while (q--) {
    cin >> mm;
    rep (i, 1, mm) cin >> rt[i];
    sort(rt + 1, rt + mm + 1, [&](int x, int y) {
      return val[x] < val[y];
    });
    rep (i, 1, mm) mx[i] = max(mx[i - 1], val[rt[i]]);
    ll ans = mx[mm], MX = 0;
    int L = rt[mm];
    per (i, mm, 1) {
      int LL = L;
      L = lca(L, rt[i]);
      MX = max(MX + LEN(LL, L), LEN(rt[i], L));
      ans = min(ans, max(MX, mx[i - 1]));
    }
    cout << ans << '\n';
  }
}

int main() {
  cin.tie(nullptr) -> ios::sync_with_stdio(false);
  int t; cin >> t;
  while (t--) work();
}