#include<bits/stdc++.h>
#define endl '\n'
//#define int long long
using namespace std;
using  i64 = long long;
using PII = pair<int, int>;
const int N = 1e5+10;
int dfn[N], fa[N][17], dep[N], ti;
i64 dis[N], dr[N];
vector<PII> g[N];
bool red[N];
template<class T> void read(T & x){
    int f=1, c; while(c = getchar(), c < 48 || 57 < c) if(c == '-') f = -1;x = c ^ 48;
    while(c = getchar(), 47 < c && c < 58) x = (x << 3) + (x << 1) + (c ^ 48);x *= f;
}
void dfs(int u, int father)
{
	dep[u] = dep[father] + 1;
	dfn[u] = ++ ti;
	fa[u][0] = father;
	for(int k = 1;k < 18;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];
}
vector<int> v;
int k;

bool check(i64 x)
{
	vector<int> st;
	for(int u : v)
		if(dr[u] > x)
			st.push_back(u);
	 // sort(st.begin(), st.end(), [&](int a, int b){
	 // 	return dfn[a] < dfn[b];
	 // });

	if(st.size() <= 1)
		return true;

	int a = st[0], b = st[0];
	for(int u : st)
	{
		if(dfn[u] < dfn[a])
			a = u;
		if(dfn[u] > dfn[b])
			b = u;
	}

	int anc = lca(a, b);

	for(int u : st)
		if(dis[u] - dis[anc] > x)
			return false;
	return true;
}

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

	for(int i = 1;i < n;i ++)
	{
		int u, v, w;
		read(u), read(v), read(w);
		g[u].push_back({v, w});
		g[v].push_back({u, w});
	}
	dfs(1, 0);
	// for(int i = 1;i <= n;i ++)
	// 	cout << "u : " << i << ' ' << dr[i] << endl; 
	while(q --)
	{
		
		read(k);
		v.clear();
		for(int i = 1, u;i <= k;i ++)
			read(u), v.push_back(u);

		i64 l = 0, r = 1e15;
		while(l < r)
		{
			i64 mid = l + r >> 1;
			if(check(mid))
				r = mid;
			else
				l = mid  + 1;
		}

		printf("%lld\n", l);
	}

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

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