#include <bits/stdc++.h>
#define fi first
#define se second
#define int long long
using namespace std;
const int N = 1e5+9;
int fa[N][21], dep[N], dis[N], n, m, q, r[N], isred[N], anc[N], nr = 1, node[N], k;
vector<pair<int, int>> adj[N];
void dfs1(int u, int f) {
	dep[u] = dep[f] + 1; fa[u][0] = f;
	if (!isred[u]) anc[u] = nr;
	for (int i = 1; i < 21; i++) fa[u][i] = fa[fa[u][i - 1]][i - 1];
	int tmp = nr;
	for (auto i : adj[u]) {
		if (i.fi == f) continue;
		if (isred[i.fi]) nr = i.fi;
		dis[i.fi] = dis[u] + i.se;
		dfs1(i.fi, u);
	}
	
	nr = tmp;
}

int lca(int x, int y) {
	if (dep[x] < dep[y]) swap(x, y);
	for (int i = 20; i > -1; i--) if (dep[fa[x][i]] >= dep[y]) x = fa[x][i];
	if (x == y) return x;
	for (int i = 20; i > -1; i--) if (fa[x][i] != fa[y][i]) x = fa[x][i], y = fa[y][i];
	return fa[x][0];
}

bool check(int lim) {
	int cc = 0;
	for (int i = 1; i <= k; i++) {
		int u = node[i];
		if (dis[u] - dis[anc[u]] <= lim) continue;
		cc++;
	}
	
	if (cc == 1) return true;
	if (cc == 0) return true;
	int zx = 0;
	for (int i = 1; i <= k; i++) {
		int u = node[i];
		if (dis[u] - dis[anc[u]] > lim) {
			if (!zx) zx = u;
			else zx = lca(zx, u);
		}
	}
	
	int mx = -1;
	for (int i = 1; i <= k; i++) {
		int u = node[i];
		if (dis[u] - dis[anc[u]] > lim) {
			mx = max(mx, dis[u]);
		}
	}
	
	return mx - dis[zx] <= lim;
}

void solve() {
	cin >> n >> m >> q;
	memset(dis, 0, sizeof(int) * (n + 9));
	memset(isred, 0, sizeof(int) * (n + 9));
	memset(dep, 0, sizeof(int) * (n + 9));
	memset(anc, 0, sizeof(int) * (n + 9));
	nr = 1;
	for (int i = 0; i <= n; i++) adj[i].clear();
	for (int i = 1; i <= m; i++) {
		cin >> r[i];
		isred[r[i]] = true;
		anc[r[i]] = r[i];
	}
	
	for (int i = 1, u, v, w; i < n; i++) {
		cin >> u >> v >> w;
		adj[u].push_back({v, w});
		adj[v].push_back({u, w});
	}
	
	dfs1(1, 0);
	
	while (q--) {
		cin >> k;
		for (int i = 1; i <= k; i++) {
			cin >> node[i];
		}
		
		int l = 0, r = 1e16, ans = 0;
		while (l <= r) {
			int mid = (l + r) >> 1;
			if (check(mid)) {
				ans = mid;
				r = mid - 1;
			} else l = mid + 1;
		}
		
		cout << ans << "\n";
	}
}

signed main() {
	//freopen("B.in", "r", stdin);
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int T; cin >> T;
	while (T--) {
		solve();
	}
	
	return 0;
}