#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 2e5 + 100;
int T, n, m, q, c[N], u, v, w, edgenum, Head[N], Next[N], vet[N], val[N], dep[N], dom[N], in[N], out[N], l, seq[N], ST[N][20], l2[N], k, p[N];
ll sum[N], dis[N];
void add(int u, int v, int w) {
	Next[++edgenum] = Head[u];
	Head[u] = edgenum;
	vet[edgenum] = v;
	val[edgenum] = w;
}
void dfs(int u, int fa, int w) {
	dep[u] = dep[fa] + 1;
	sum[u] = sum[fa] + w;
	if (c[u]) dom[u] = u, dis[u] = 0;
	else dom[u] = dom[fa], dis[u] = dis[fa] + w;
	seq[in[u]=++l] = u;
	for (int e=Head[u]; e; e=Next[e]) {
		int v=vet[e];
		if (v ^ fa) dfs(v, u, val[e]), seq[++l] = u;
	} out[u] = l;
}
bool chk(ll x) {
	int Min = 1e9, Max = 0;
	for (int i=1; i<=k; i++) if (dis[p[i]] > x)
		Min = min(Min, in[p[i]]), Max = max(Max, in[p[i]]);
	int t = l2[Max-Min+1], LCA = ST[Min][t], _LCA = ST[Max-(1<<t)+1][t];
	if (dep[_LCA] < dep[LCA]) LCA = _LCA;
	for (int i=1; i<=k; i++) if (dis[p[i]] > x && sum[p[i]] - sum[LCA] > x) return 0;
	return 1;
}
int main() {
	cin >> T;
	while (T --) {
		scanf ("%d%d%d", &n, &m, &q);
		for (int i=1; i<=n; i++) c[i] = Head[i] = 0; edgenum = l = 0;
		while (m --) scanf ("%d", &u), c[u] = 1;
		for (int i=1; i<n; i++)
			scanf ("%d%d%d", &u, &v, &w), add(u, v, w), add(v, u, w);
		dfs(1, 0, 0);
		l2[0] = - 1;
		for (int i=1; i<=l; i++) ST[i][0] = seq[i], l2[i] = l2[i>>1] + 1;
		for (int j=1; j<=l2[l]; j++) for (int i=1; i<=l; i++) {
			ST[i][j] = ST[i][j-1];
			if (i + (1 << j - 1) <= l && dep[ST[i+(1<<j-1)][j-1]] < dep[ST[i][j]])
				ST[i][j] = ST[i+(1<<j-1)][j-1];
		}
		while (q --) {
			scanf ("%d", &k);
			for (int i=1; i<=k; i++) {
				scanf ("%d", &p[i]);
				if (c[p[i]]) i --, k --;
			}
			if (k <= 1) { puts ("0"); continue; }
			ll L = 0, R = 0;
			for (int i=1; i<=k; i++)
				R = max(R, dis[p[i]]);
			while (L < R) {
				ll mid = L + R >> 1;
				chk(mid) ? R = mid : L = mid + 1;
			} printf ("%lld\n", R);
		}
	}
}