/**
 *  - Meet Brahmbhatt
 *  - Hard work always pays off
**/
#include"bits/stdc++.h"
using namespace std;

#ifdef MeetBrahmbhatt
#include "debug.h"
#else
#define dbg(...) 72
#endif

#define endl "\n"
#define int long long

const long long INF = 4e18;


template <int LOGN>
struct Lca {
    int n;
    vector<int> dep;
    vector<int> PAR;
    vector<int> L, R;
    vector<vector<pair<int, int>>> G;
    vector<vector<int>> up;
    int T = 0;
    Lca(const vector<vector<pair<int, int>>> &adj) {
        n = (int) adj.size();
        PAR.resize(n);
        dep.resize(n);
        L.resize(n);
        R.resize(n);
        G = adj;
        up.assign(LOGN, vector<int>(n, -1));
        dfs(0, -1);
    }
    inline void dfs (int u, int par) {
        PAR[u] = par;
        L[u] = T++;
        for (int i = 1; i < LOGN; i++) {
            if (up[i - 1][u] != -1) {
                up[i][u] = up[i - 1][up[i - 1][u]];
            }
        }
        for (auto &[to, w] : G[u]) {
            if (to != par) {
                up[0][to] = u;
                dep[to] = dep[u] + 1;
                dfs(to, u);
            }
        }
        R[u] = T;
    }
    bool is_ancestor(int u, int v) const {
        return L[u] <= L[v] && R[v] <= R[u];
    }
    inline int kth(int u, int k) {
        for (int i = 0; i < LOGN; i++) {
            if (k >> i & 1) {
                u = up[i][u];
                if (u == -1) {
                    return -1ll;
                }
            }
        }
        return u;
    }
    inline int lca(int x, int y) {
        if (dep[x] < dep[y]) swap(x, y);
        int d = dep[x] - dep[y];
        x = kth(x, d);
        if (x == y) return x;
        for (int i = LOGN - 1; i >= 0; i--) {
            if (up[i][x] != up[i][y]) {
                x = up[i][x];
                y = up[i][y];
            }
        }
        return up[0][x];
    }
    inline int dis(int u, int v) {
        return dep[u] + dep[v] - 2 * dep[lca(u, v)];
    }
};


void solve() {
    int n, m, q;
    cin >> n >> m >> q;

    vector<int> red(n);
    for (int i = 0; i < m; i++) {
        int x;
        cin >> x;
        red[x - 1] = 1;
    }

    vector<vector<pair<int, int>>> G(n);
    for (int i = 0; i < n - 1; i++) {
        int u, v, w;
        cin >> u >> v >> w;
        u--; v--;
        G[u].push_back({v, w});
        G[v].push_back({u, w});
    }

    vector<int> ances(n);
    vector<int> cost(n);
    vector<int> dep(n);

    function<void(int, int, int)> dfs = [&] (int u, int par, int prev) {
        if (red[u]) {
            prev = u;
            cost[u] = 0;
        }
        ances[u] = prev;
        for (auto [to, w] : G[u]) {
            if (to != par) {
                cost[to] = cost[u] + w;
                dep[to] = dep[u] + w;
                dfs(to, u, prev);
            }
        }
    };
    dfs(0, -1, 0);

    Lca<20> T(G);
    while (q--) {
        int K;
        cin >> K;
        vector<int> nodes(K);
        for (int &i : nodes) {
            cin >> i;
            i--;
        }
        int mx = nodes[0];
        for (int i = 0; i < K; i++) {
            if (cost[nodes[i]] > cost[mx]) {
                mx = nodes[i];
            }
        }
        vector<int> sub;
        int other = 0;
        for (int i = 0; i < K; i++) {
            if (ances[nodes[i]] == ances[mx]) {
                sub.push_back(nodes[i]);
            } else {
                other = max(other, cost[nodes[i]]);
            }
        }
        int sz = (int) sub.size();

        vector<int> I(sz);
        iota(I.begin(), I.end(), 0);
        sort(I.begin(), I.end(), [&] (int x, int y) {return T.L[sub[x]] < T.L[sub[y]]; });

        vector<int> pref(sz + 1), suf(sz + 1);
        for (int i = 0; i < sz; i++) {
            pref[i + 1] = max(pref[i], cost[sub[I[i]]]);
        }
        for (int i = sz - 1; i >= 0; i--) {
            suf[i] = max(suf[i + 1], cost[sub[I[i]]]);
        }

        vector<int> Time;
        for (int i = 0; i < sz; i++) {
            Time.push_back(T.L[sub[I[i]]]);
        }

        int res = INF;
        for (int i = 0; i < sz; i++) {
            int z = T.lca(mx, sub[I[i]]);
            int nval = cost[mx] - (dep[z] - dep[ances[mx]]);
            int L = (int) (lower_bound(begin(Time), end(Time), T.L[z]) - begin(Time));
            int R = (int) (lower_bound(begin(Time), end(Time), T.R[z]) - begin(Time)) - 1;
            res = min(res, max({other, pref[L], suf[R + 1], nval}));
        }
        cout << res << endl;
    }
}

signed main() {
    cin.tie(0)->sync_with_stdio(0);
    cout << fixed << setprecision(9);
    int tt = 1;
    cin >> tt;
    while (tt--) solve();
    return 0;
}