#include<bits/stdc++.h>

using namespace std;

typedef long long ll;

struct pt {
    int lca;
    ll w_pref, best_pref;
};

int const maxn = 1e5 + 5, logg = 17;
vector < pair < int, int > > g[maxn];
ll pref[maxn];
int tin[maxn], tout[maxn], cur, h[maxn], up[maxn][logg];
ll value[maxn];
int mark[maxn];

void dfs(int v, int p, ll best) {
    tin[v] = cur++;
    up[v][0] = p;
    h[v] = h[p] + 1;
    if (mark[v]) best = pref[v];
    value[v] = best;
    for (int j = 1; j < logg; j++) up[v][j] = up[up[v][j - 1]][j - 1];
    for (auto [u, w] : g[v]) {
        if (u == p) continue;
        pref[u] = pref[v] + w;
        dfs(u, v, best);
    }
    tout[v] = cur++;
}

int get_la(int v, int x) {
    for (int i = 0; i < logg; i++) {
        if ((x>>i)&1) v = up[v][i];
    }
    return v;
}

int get_lca(int v, int u) {
    if (h[v] > h[u]) v = get_la(v, h[v] - h[u]);
    else u = get_la(u, h[u] - h[v]);
    if (u == v) return u;
    for (int i = logg - 1; i >= 0; i--) {
        if (up[v][i] != up[u][i]) v = up[v][i], u = up[u][i];
    }
    return up[v][0];
}

main() {
#ifdef HOME
    freopen("input.txt", "r", stdin);
#endif // HOME
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int t;
    cin >> t;
    while (t--) {
        int n, m, q, u, v, w;
        cin >> n >> m >> q;
        for (int i = 1; i <= n; i++) g[i] = {}, mark[i] = 0;
        for (int i = 1; i <= m; i++) {
            cin >> u;
            mark[u] = 1;
        }
        for (int i = 1; i < n; i++) {
            cin >> u >> v >> w;
            g[u].push_back({v, w});
            g[v].push_back({u, w});
        }
        dfs(1, 0, 0);
        for (int i = 1; i <= q; i++) {
            int k;
            cin >> k;
            vector < int > node;
            for (int j = 1; j <= k; j++) {
                cin >> u;
                node.push_back(u);
            }
            int mx = node[0];
            for (auto key : node) {
                if (pref[key] - value[key] > pref[mx] - value[mx]) mx = key;
            }
            ll ans = pref[mx] - value[mx];
            vector < pt > all_lca;
            for (auto key : node) {
                all_lca.push_back({get_lca(mx, key), pref[key], value[key]});
            }
            ll cur = 0;
            sort(all_lca.begin(), all_lca.end(), [](pt s, pt f) {
                return h[s.lca] > h[f.lca];
            });
            int l = 0;
            set < pair < ll, ll > > Q;
            multiset < ll > mx_value;
            vector < ll > suff(k + 1);
            for (int i = k - 1; i >= 0; i--) {
                suff[i] = max(suff[i + 1], all_lca[i].w_pref - all_lca[i].best_pref);
            }
            while (l < k) {
                int r = l;
                while (r < k && all_lca[l].lca == all_lca[r].lca) {
                    Q.insert({all_lca[r].best_pref, all_lca[r].w_pref});
                    mx_value.insert(all_lca[r].w_pref);
                    r++;
                }
                int now = all_lca[l].lca;
                while (!Q.empty()) {
                    auto p = *Q.rbegin();
                    if (p.first >= pref[now]) {
                        cur = max(cur, p.second - p.first);
                        mx_value.erase(mx_value.find(p.second));
                        Q.erase(p);
                    } else break;
                }
                ll res = cur;
                if (!Q.empty()) res = max(res, *mx_value.rbegin() - pref[now]);
                res = max(res, suff[r]);
                ans = min(ans, res);
                l = r;
            }
            cout << ans << '\n';
        }
    }
    return 0;
}