#include<bits/stdc++.h>
#define endl '\n'
//#define int long long
using namespace std;
using  i64 = long long;
using PII = pair<i64, int>;
const int N = 1e5 + 10;
int n, m, q;
vector<PII> g[N];
bool red[N];
i64 fa[N][17], dep[N], dis[N], dr[N];
i64 dfn[N], cnt;
void dfs(int u, int father)
{
	dfn[u] = ++ cnt;
	dep[u] = dep[father] + 1;
	fa[u][0] = father;
	for(int k = 1;k < 17;k ++)
		fa[u][k] = fa[fa[u][k - 1]][k - 1];

	if(red[u])
		dr[u] = 0;
	for(auto [v, w] : g[u])
	{
		if(v == father)
			continue;
		dis[v] = dis[u] + w;
		dr[v] = dr[u] + w;
		dfs(v, u);
	}
}

int lca(int a, int b)
{
	 if(dep[a] < dep[b])
	 	swap(a, b);

	 for(int k = 16;k >= 0;k --)
	 	if(dep[fa[a][k]] >= dep[b])
	 		a = fa[a][k];

	 if(a == b)
	 	return a;

	 for(int k = 16;k >= 0;k --)
	 	if(fa[a][k] != fa[b][k])
	 		a = fa[a][k], b = fa[b][k];

	 return fa[a][0];
}

void solve()
{
	cin >> n >> m >> q;
	for(int i = 1, v;i <= m;i ++)
		cin >> v, red[v] = true;

	for(int i = 1;i < n;i ++)
	{
		int u, v, w;
		cin >> u >> v >> w;
		g[u].push_back({v, w});
		g[v].push_back({u, w});
	}

	dfs(1, 0);

	while(q --)
	{
		int k;
		cin >> k;
		vector<int> v(k);
		for(int & x : v)
			cin >> x;
		sort(v.begin(), v.end(), [&](int a, int b) {
			return dr[a] > dr[b];
		});
		v.push_back(0);
		i64 res = dr[v[1]], mx = dis[v[0]];
		int anc = v[0];
		for(int i = 1;i + 1 < v.size();i ++)
		{
			anc = lca(anc, v[i]);
			mx = max(mx, dis[v[i]]);
			res = min(res, max(dr[v[i + 1]], mx - dis[anc]));

		}

		cout << res << endl;
	}

	for(int i = 1;i<= n;i ++)
		red[i] = false, g[i].clear();
	cnt = 0;

}

int main()
{
	ios::sync_with_stdio(false), cin.tie(0);
	int tc;
	cin >> tc;
	while(tc --)
		solve();
	return 0;
}