#include <bits/stdc++.h>
using namespace std;
using ll = long long;

const int mod = 998244353;
const int N = 1e5 + 5;

int n, m, q;
int red[N], p[N], faz[20][N], d[N];
ll cost[N];
ll dep[N];
vector<pair<int, int>> G[N];

void pre(int u, int fa, ll ld) {
    if (red[u]) ld = dep[u];
    cost[u] = dep[u] - ld;
   // cout << u << ' ' << cost[u] << '\n';
    faz[0][u] = fa;
    for (int i = 1; i < 20; i++) faz[i][u] = faz[i - 1][faz[i - 1][u]];
    for (auto [v, w] : G[u]) if (v != fa) {
        dep[v] = dep[u] + w;
        d[v] = d[u] + 1;
        pre(v, u, ld);
    }
}
int LCA(int u, int v) {
    if (d[u] < d[v]) swap(u, v);
    int det = d[u] - d[v];
    for (int i = 0; i < 20; i++) if ((det >> i) & 1) u = faz[i][u];
    if (u == v) return u;
    for (int i = 19; i >= 0; i--) if (faz[i][u] != faz[i][v]) {
        u = faz[i][u];
        v = faz[i][v];
    }
    return faz[0][u];
}

void solve() {
    cin >> n >> m >> q;
    for (int i = 1; i <= n; i++) G[i].clear(), red[i] = 0;
    for (int i = 1; i <= m; i++) {
        int x;
        cin >> x;
        red[x] = 1;
    }
    for (int i = 1; i < n; i++) {
        int u, v, w;
        cin >> u >> v >> w;
        G[u].push_back({v, w});
        G[v].push_back({u, w});
    }
    pre(1, 0, 0);
   // for (int i = 1; i <= n; i++) cout << cost[i] << " \n"[i == n];
    while (q--) {
        int k;
        cin >> k;
        for (int i = 1; i <= k; i++) cin >> p[i];
        sort(p + 1, p + k + 1, [](int x, int y) {
            return cost[x] > cost[y];
        });
        int po = 1, lca = p[1];
        ll now = dep[p[1]], mx = dep[p[1]];
        ll ans = (k == 1 ? 0 : cost[p[2]]);
        while (po < k && cost[p[po + 1]] > mx - now) {
            po++;
            ans = min(ans, cost[p[po]]);
            lca = LCA(lca, p[po]);
            //cout << "* " << lca << '\n';
            now = dep[lca];
            mx = max(mx, dep[p[po]]);
        }
        ans = min(ans, mx - now);
        cout << ans << '\n';
    }
}

int main() {
    ios::sync_with_stdio(0), cin.tie(0);
    int T = 1;
    cin >> T;
    while (T--) solve();
    return 0;
}