#include<bits/stdc++.h>
#define int long long
#define endl '\n'
#define PII pair<int,int>
using namespace std;
const int maxn = 1e6 + 5;
const int mod = 998244353;
struct edge {
	int v, w;
};
vector<edge> tr[maxn];
bool sta[maxn];
int dep[maxn], f[maxn][30], c[maxn][30];
void ini(int u, int fa) {
	dep[u] = dep[fa] + 1;
	f[u][0] = fa;
	for (int i = 1; i <= 25; ++i) {
		f[u][i] = f[f[u][i - 1]][i - 1];
		c[u][i] = c[f[u][i - 1]][i - 1] + c[u][i - 1];
	}
	for (edge e : tr[u]) {
		int v = e.v;
		int w = e.w;
		if (v == fa) continue;
		c[v][0] = w;
		ini(v, u);
	}
}
int lca(int u, int v) {
	if (dep[u] < dep[v]) swap(u, v);
	for (int i = 25; i >= 0; --i) {
		if (dep[f[u][i]] < dep[v]) continue;
		u = f[u][i];
	}
	if (u == v) return u;
	for (int i = 25; i >= 0; --i) {
		if (f[u][i] == f[v][i]) continue;
		u = f[u][i];
		v = f[v][i];
	}
	return f[u][0];
}
int get(int u, int aim) {
	int res = 0;
	for (int i = 25; i >= 0; --i) {
		if (dep[f[u][i]] < dep[aim]) continue;
		res += c[u][i];
		u = f[u][i];
	}
	return res;
}
int ans[maxn];
void dfs(int u, int d, int fa) {
	if (!sta[u]) ans[u] = d;
	else ans[u] = 0;
	for (edge e : tr[u]) {
		int v = e.v;
		int w = e.w;
		if (v == fa) continue;
		if (sta[u]) dfs(v, w, u);
		else dfs(v, d + w, u);
	}
}
vector<int> t;
bool check(int mid) {
	vector<int> te;
	for (int i = 0; i < t.size(); ++i) {
		if (ans[t[i]] > mid) {
			te.push_back(t[i]);
		}
	}
	if (te.size() <= 1) return true;
	int an = te[0];
	for (int i = 1; i < te.size(); ++i) {
		an = lca(te[i], an);
	}
	for (int i = 0; i < te.size(); ++i) {
		if (get(t[i], an) > mid) return false;
	}
	return true;
}
void solve() {
	int n, m, q;
	cin >> n >> m >> q;
	for (int i = 1; i <= n; ++i) {
		tr[i].clear();
		sta[i] = false;
		for (int j = 0; j <= 25; ++j) {
			f[i][j] = 0;
			c[i][j] = 0;
		}
	}
	for (int i = 1; i <= m; ++i) {
		int a; cin >> a;
		sta[a] = true;
	}
	for (int i = 1; i < n; ++i) {
		int u, v, w;
		cin >> u >> v >> w;
		tr[u].push_back({ v,w });
		tr[v].push_back({ u,w });
	}
	ini(1, 0);
	dfs(1, 0, 0);
	while (q--) {
		int k; cin >> k;
		t.clear();
		for (int i = 0; i < k; i++) {
			int a; cin >> a;
			t.push_back(a);
		}
		int l = 0, r = 1e15, res = LLONG_MAX;
		while (l <= r) {
			int mid = l + r >> 1;
			if (check(mid)) {
				r = mid - 1;
				res = mid;
			}
			else l = mid + 1;
		}
		cout << res << endl;
	}
}
signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0); cout.tie(0);
	int T; cin >> T;
	while (T--) {
		solve();
	}
	return 0;
}