#include <bits/stdc++.h>
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define st first
#define nd second
using namespace std;
typedef long long ll;
const int mod = 1e9 + 7;
const int N = 1e6 + 5;
const int LG = 17;
vector<pair<int, int>> adj[N];
ll cost[N];
int isr[N], idx[N], curc = 0;
int par[LG][N], dp[N];

int lca(int u, int v) {
	if (dp[u] < dp[v])
		swap(u, v);
	int d = dp[u] - dp[v];
	for (int i = 0; i < LG; i++)
		if (d >> i & 1)
			u = par[i][u];
	if (u == v)
		return u;
	for (int i = LG - 1; i >= 0; i--)
		if (par[i][u] != par[i][v])
			u = par[i][u], v = par[i][v];
	return par[0][u];
}

void dfs(int u, int p, ll d, int col) {
	if (isr[u])
		d = 0;
	if (p != -1 && isr[p])
		col = ++curc;
	if (p != -1) {
		dp[u] = dp[p] + 1;
		par[0][u] = p;
	}
	cost[u] = d;
	idx[u] = col;
	for (auto [v, w]: adj[u]) {
		if (v == p) continue;
		dfs(v, u, w + d, col);
	}
}

void solve() {
	int n, m, q; cin >> n >> m >> q;
	curc = 0;
	for (int i = 0; i < n; i++)
		adj[i].clear(), isr[i] = 0;
	for (int i = 0; i < m; i++) {
		int u; cin >> u; u--;
		isr[u] = 1;
	}
	for (int i = 1; i < n; i++) {
		int u, v, w; cin >> u >> v >> w;
		u--, v--;
		adj[u].push_back({v, w});
		adj[v].push_back({u, w});
	}
	dfs(0, -1, 0, 0);
	for (int i = 1; i < LG; i++) {
		for (int j = 0; j < n; j++)
			par[i][j] = par[i - 1][par[i - 1][j]];
	}
	while (q--) {
		int k; cin >> k;
		vector<int> arr(k);
		int bi = 0;
		for (int i = 0; i < k; i++) {
			int u; cin >> u; u--;
			if (cost[u] > cost[arr[bi]])
				bi = i;
			arr[i] = u;
		}
		ll ans = 0;
		vector<pair<ll, ll>> tmp;
		for (int i = 0; i < k; i++) {
			if (idx[arr[i]] != idx[arr[bi]])
				ans = max(ans, cost[arr[i]]);
			else {
				int l = lca(arr[bi], arr[i]);
				tmp.push_back({-cost[l], cost[arr[i]]});
//				cerr << arr[i]+1 << " " << arr[bi]+1 << " -> " << l+1 << " : " << cost[l] << endl;
			}
		}
		if (ans != cost[arr[bi]]) {
			sort(tmp.begin(), tmp.end());
			vector<ll> rem(sz(tmp) + 1);
			for (int i = sz(tmp) - 1; i >= 0; i--)
				rem[i] = max(rem[i + 1], tmp[i].second);
			ll val = cost[arr[bi]];
			for (int i = 0; val > ans && i < sz(tmp); i++)
				val = min(val, max(rem[i + 1], cost[arr[bi]] + tmp[i].first));
			ans = max(ans, val);
		}
		cout << ans << "\n";
	}
}

int main() {
	ios_base::sync_with_stdio(false); cin.tie(0);
	int t; cin >> t; while (t--) solve();
}