#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <iostream>
#include <map>
#include <set>
#include <vector>

#define X first
#define Y second
#define PB push_back

using namespace std;

typedef long long ll;
typedef pair < int, int > pii;
typedef vector < int > vi;
typedef pair < ll, int > pli;

const int N = 1e5 + 500;
const int M = 1e6 + 500;
const int LOG = 18;
const int OFF = (1 << 20);
const int INF = 0x3f3f3f3f;
const ll LINF = (ll)1e18;
const int MOD = 1e9 + 7; // 998244353

inline int add(int A, int B) {
    if(A + B >= MOD)
        return A + B - MOD;
    return A + B;
}

inline int sub(int A, int B) {
	if(A - B < 0)
		return A - B + MOD;
	return A - B;
}

inline int mul(int A, int B) {
	return (ll)A * B % MOD;
}

inline int pot(int A, int B) {
	int ret = 1, bs = A;
	for(;B;B >>= 1) {
		if(B & 1) ret = mul(ret, bs);
		bs = mul(bs, bs);
	}
	return bs;
}

int n, m, q, dep[M];
ll dis[N], rd[N];
vector < pli > v[N];
int par[N][LOG];


void dfs(int x, int lst, ll zad){
	if(rd[x] == -1) rd[x] = dis[x] - zad; 
	else zad = dis[x];
	par[x][0] = lst;
	for(auto nxt : v[x]) {
		if(nxt.Y == lst) continue;
		dep[nxt.Y] = dep[x] + 1;
		dis[nxt.Y] = dis[x] + nxt.X;
		dfs(nxt.Y, x, zad);
	}
}

void prepare_lca(){
	for(int j = 1;j < LOG;j++) {
		for(int i = 1;i <= n;i++) {
			par[i][j] = par[par[i][j - 1]][j - 1];
		}
	}
}

inline int get_lca(int x, int y) {
	if(dep[x] < dep[y]) swap(x, y);
	for(int i = 17;i >= 0;i--)
		if(dep[x] - (1 << i) >= dep[y]) x = par[x][i];
	if(x == y) return x;
	for(int i = 17;i >= 0;i--)
		if(par[x][i] != par[y][i]) x = par[x][i], y = par[y][i];
	return par[x][0];
}

bool cmp(int x, int y) {
	return rd[x] > rd[y];
}

void solve(){
	scanf("%d%d%d", &n, &m, &q);
	for(int i = 1;i <= n;i++) rd[i] = -1;
	for(;m--;) {
		int x; scanf("%d", &x); rd[x] = 0;
	}
	for(int i = 1;i < n;i++) {
		int a, b, c; scanf("%d%d%d", &a, &b, &c);
		v[a].PB({c, b}); v[b].PB({c, a});
	}
	
	dfs(1, 1, 0); prepare_lca();
	for(;q--;) {
		int ln; scanf("%d", &ln);
		vector < int > v;
		ll ans = 0;
		for(;ln--;) {
			int x; scanf("%d", &x); v.PB(x);
			ans = max(ans, rd[x]);
		}
		sort(v.begin(), v.end(), cmp);
		int lc = v[0];
		ll najdub = dis[v[0]];
		for(int i = 0;i < (int)v.size();i++) {
			lc = get_lca(v[i], lc);
			najdub = max(najdub, dis[v[i]]);
			ans = min(ans, max(i + 1 < (int)v.size() ? rd[v[i + 1]] : 0,
							  najdub - dis[lc]));
		}
		printf("%lld\n", ans);
	}
	for(int i = 1;i <= n;i++) v[i].clear();
}


int main(){
    //ios_base::sync_with_stdio(false);
    //cin.tie(0);
	//int T = 1;
	int T; scanf("%d", &T);
    for(;T--;) solve();
    return 0;
}