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

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, int> pli;
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define len(x) (int) x.size()
#define pb push_back
mt19937 rnd(time(0));

const int N = 1e5 + 7, LG = 19;
int n, m, q, h[N], par[LG][N];
vector<pii> adj[N];
bool col[N];
ll dis[N], c[N];

void read_input() {
	cin >> n >> m >> q;
	for (int i = 0; i < n; i++) {
		adj[i].clear();
		col[i] = false;
		dis[i] = 0;
	}
	for (int i = 0; i < m; i++) {
		int r;
		cin >> r;
		col[--r] = true;
	}
	for (int i = 1; i < n; i++) {
		int u, v, w;
		cin >> u >> v >> w;
		u--, v--;
		adj[u].pb({v, w});
		adj[v].pb({u, w});
	}
}

void dfs(int u, int p = -1, int lst = 0) {
	c[u] = dis[u] - dis[lst];
	for (int i = 1; i < LG; i++)
		par[i][u] = par[i - 1][par[i - 1][u]];
	for (auto [v, w]: adj[u])
		if (v != p) {
			dis[v] = w + dis[u];
			par[0][v] = u;
			h[v] = 1 + h[u];
			dfs(v, u, (col[v]? v: lst));
		}
}

int lca(int u, int v) {
	if (h[u] < h[v])
		swap(u, v);
	for (int i = 0; i < LG; i++)
		if (((h[u] - h[v]) >> i) & 1)
			u = par[i][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 u == v? u: par[0][u];
}

void solve() {
	dfs(0);
	while (q--) {
		int k;
		cin >> k;
		vector<pli> vec;
		for (int i = 0; i < k; i++) {
			int u;
			cin >> u;
			u--;
			vec.pb({c[u], u});
		}
		sort(all(vec));
		ll ans = vec.back().F;
		int lc = vec.back().S;
		ll mx = 0;
		for (int i = k - 1; i >= 0; i--) {
			lc = lca(lc, vec[i].S);
			mx = max(mx, dis[vec[i].S]);
			ll tmp = mx - dis[lc];
			if (i)
				tmp = max(tmp, vec[i - 1].F);
			ans = min(ans, tmp);
		}
		cout << ans << '\n';
	}
}

int32_t main() {
	ios:: sync_with_stdio(0), cin.tie(0), cout.tie(0);
	int t;
	cin >> t;
	while (t--)
		read_input(), solve();
	return 0;
}