#include <bits/stdc++.h>

using namespace std;

#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define RFOR(i, a, b) for(int i = (a) - 1; i >= (b); i--)
#define SZ(a) int(a.size())
#define ALL(a) a.begin(), a.end()
#define PB push_back
#define MP make_pair
#define F first	
#define S second

typedef long long LL;
typedef vector<int> VI;
typedef pair<int, int> PII;
typedef double db;

const int INF = 1'000'000'447;
const LL LINF = (LL)INF * INF;
const int N = 100'447;
const int LOG = 17;
vector<PII> g[N];
LL d[N];
LL cost[N];
bool red[N];
int tin[N];
int tout[N];
int up[LOG][N];
int T = 0;

void dfs(int v, LL c, LL h, int p)
{
	if (red[v])
		c = 0;
	cost[v] = c;
	d[v] = h;
	tin[v] = T++;
	up[0][v] = p;
	FOR (i, 1, LOG)
	{
		up[i][v] = up[i - 1][up[i - 1][v]];
	}
	for (auto [to, w] : g[v])
	{
		if (to != p)
		{
			dfs(to, c + w, h + w, v);
		}
	}
	tout[v] = T++;
}

bool is_par(int p, int v)
{
	return tin[p] <= tin[v] && tout[v] <= tout[p];
}

int lca(int v, int u)
{
	if (is_par(v, u))
		return v;
	RFOR (i, LOG, 0)
	{
		if (!is_par(up[i][v], u))
			v = up[i][v];
	}
	return up[0][v];
}

void solve()
{
	int n, m, q;
	cin >> n >> m >> q;
	FOR (i, 0, m)
	{
		int x;
		cin >> x;
		red[x - 1] = true;
	}
	FOR (i, 0, n - 1)
	{
		int a, b, w;
		cin >> a >> b >> w;
		a--, b--;
		g[a].PB({b, w});
		g[b].PB({a, w});
	}
	dfs(0, 0, 0, 0);
	FOR (i, 0, q)
	{
		int k;
		cin >> k;
		VI v(k);
		FOR (j, 0, k)
		{
			cin >> v[j];
			v[j]--;
		}
		sort(ALL(v), [&](int a, int b)
		{
			return cost[a] > cost[b];
		});
		LL ans = cost[v[0]];
		int lc = v[0];
		LL D = d[v[0]];
		FOR (j, 0, k)
		{
			lc = lca(lc, v[j]);
			D = max(D, d[v[j]]);
			LL x = D - d[lc];
			if (j + 1 != k)
				x = max(x, cost[v[j + 1]]);
			ans = min(ans, x);
		}
		cout << ans << '\n';
	}
	FOR (i, 0, n)
	{
		g[i].clear();
		cost[i] = 0;
		d[i] = 0;
		FOR (j, 0, LOG)
			up[j][i] = 0;
		tin[i] = 0;
		tout[i] = 0;
		red[i] = false;
	}
	T = 0;
}

int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout << fixed << setprecision(15);
	
	int t;
	cin >> t;
	while (t--)
	{
		solve();
	}
	
	return 0;
}