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

typedef long long ll;

const int MAXN = 1e5 + 10, MAXBIT = 18;

ll t, n, m, k, q, par[MAXN], near[MAXN], h[MAXN], dp[MAXN][MAXBIT], dist[MAXN][MAXBIT];
int cnt, st[MAXN], ed[MAXN];
vector<pair<int, int>> adj[MAXN];
vector<int> num;
bool red[MAXN];

void setup() {
	for (int i = 0; i < n; i++) {
		red[i] = near[i] = cnt = 0;
		adj[i].clear();
	}
}

void input() {
	cin >> n >> m >> q;
	setup();
	for (int i = 0; i < m; i++) {
		int u;
		cin >> u;
		red[--u] = true;	
	}
	for (int i = 0; i < n - 1; i++) {
		int u, v, w;
		cin >> u >> v >> w;
		adj[--u].push_back({--v, w});
		adj[v].push_back({u, w});	
	}
}

void calcDp(int u) {
	dp[u][0] = par[u];
	for (int i = 1; i < MAXBIT; i++) {
		dp[u][i] = dp[dp[u][i - 1]][i - 1];
		dist[u][i] = dist[u][i - 1] + dist[dp[u][i - 1]][i - 1];
	}
}

void dfs(int u, int p, ll d) {
	st[u] = cnt;
	cnt++;
	par[u] = p;
	if (!red[u])
		near[u] = near[p] + d;
	dist[u][0] = d;
	calcDp(u);	
	for (auto x : adj[u])
		if (x.first != p) {
			h[x.first] = h[u] + 1;
			dfs(x.first, u, x.second);
		}
	ed[u] = cnt;
	cnt++;
}

bool check(ll x) {
	int v = -1, ma = -1;
	for (auto u : num)
		if (near[u] > x) {
			ll w = u, sum = 0;
			for (int i = MAXBIT - 1; i >= 0; i--)
				if (sum + dist[w][i] <= x) {
					sum += dist[w][i];
					w = dp[w][i];
				}
			if (v == -1 || h[w] > ma) {
				v = w;
				h[w] = ma;	
			}
		}
	if (v == -1)
		return true;
	for (auto u : num)
		if (near[u] > x) {
			if (!(st[v] <= st[u] && ed[v] >= st[u]))	
				return false;
		}
	return true;
}

ll findAns() {
	ll l = -1, r = 1e14;
	while (r - l > 1) {
		ll mid = (l + r) / 2;
		if (check(mid))
			r = mid;
		else
			l = mid;
	}
	return r;
}

int main() {
	ios::sync_with_stdio(false); cin.tie(0);
	cin >> t;
	for (int i = 0; i < t; i++) {
		input();
		dfs(0, 0, 0);
		for (int j = 0; j < q; j++) {
			cin >> k;
			num.clear();
			for (int l = 0; l < k; l++) {
				int u;
				cin >> u;
				num.push_back(--u);
			}
			cout << findAns() << '\n';
		}
	}
	return 0;	
}