#include <bits/stdc++.h>

using namespace std;

using i64 = int64_t;

void solve() {
    int n, m, q;
    cin >> n >> m >> q;
    vector<bool> red(n);
    vector<vector<pair<int, int>>> adj(n);
    for (int i = 0; i < m; i++) {
        int x;
        cin >> x;
        x--;
        red[x] = 1;
    }
    for (int i = 0; i < n - 1; i++) {
        int u, v, w;
        cin >> u >> v >> w;
        u--, v--;
        adj[u].emplace_back(v, w), adj[v].emplace_back(u, w);
    }
    struct node {
        int dep, fa, jump;
        i64 wdep;
    };
    vector<node> tr(n);
    vector<i64> rwdep(n);
#define dep(u) (tr[u].dep)
#define jump(u) (tr[u].jump)
#define fa(u) (tr[u].fa)
#define wdep(u) (tr[u].wdep)
    function<void(int)> dfs = [&](int u) {
        int j;
        if (red[u]) rwdep[u] = 0;
        if (dep(u) - dep(jump(u)) == dep(jump(u)) - dep(jump(jump(u)))) {
            j = jump(jump(u));
        } else j = u;
        for (auto [v, w] : adj[u]) {
            if (v == fa(u)) continue;
            fa(v) = u, dep(v) = dep(u) + 1, wdep(v) = wdep(u) + w, jump(v) = j;
            rwdep[v] = rwdep[u] + w;
            dfs(v);
        }
    };
    dfs(0);
    auto find = [&](int u, int d) {
        while (dep(u) > d) {
            if (dep(jump(u)) < d) u = fa(u);
            else u = jump(u);
        }
        return u;
    };
    auto lca = [&](int u, int v) {
        if (dep(u) > dep(v)) swap(u, v);
        v = find(v, dep(u));
        while (u != v) {
            if (jump(u) == jump(v)) {
                u = fa(u), v = fa(v);
            } else {
                u = jump(u), v = jump(v);
            }
        }
        return u;
    };
    while (q--) {
        int k;
        cin >> k;
        vector<int> pnts(k);
        for (int i = 0; i < k; i++) {
            cin >> pnts[i], pnts[i]--;
        }
        sort(pnts.begin(), pnts.end(),
             [&](int u, int v) { return rwdep[u] < rwdep[v]; });
        int t = k - 1, l = pnts[k - 1];
        i64 tmp = 0, ans = rwdep[pnts[k - 1]];
        for (; t >= 0; t--) {
            int nl = lca(l, pnts[t]);
            tmp += wdep(l) - wdep(nl);
            tmp = max(tmp, wdep(pnts[t]) - wdep(nl));
            ans = min(ans, max(t == 0 ? 0 : rwdep[pnts[t - 1]], tmp));
            l = nl;
        }
        cout << ans << "\n";
    }
    // cout << "\n";
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int t = 1;
    cin >> t;
    while (t--) {
        solve();
    }
}