#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define MAXN 100005
int T, t, n, m, q, k;
ll dp[MAXN], dep[MAXN];
int id[MAXN], tot, lg[MAXN], f[MAXN][20], dep1[MAXN];
vector<pair<int, int>> e[MAXN];
bool vis[MAXN], red[MAXN];
void push(int x, int y, int w) {
	e[x].push_back({y, w});
	e[y].push_back({x, w});
}
void dfs(int x, int fa, ll dis) {
	f[x][0] = fa;
	id[x] = ++tot;
	if(red[x]) dis = dep[x];
	dp[x] = dep[x] - dis;
	dep1[x] = dep1[fa] + 1;
	for(int i=1;i<=lg[dep1[x]];i++) f[x][i] = f[f[x][i-1]][i-1];
	for(auto [v, w] : e[x]) {
		if(v == fa) continue;
		dep[v] = dep[x] + w;
		dfs(v, x, dis);
	}
}
int lca(int x, int y) {
	if(dep1[x] < dep1[y]) swap(x, y);
	while(dep1[x] != dep1[y]) x = f[x][lg[dep1[x]-dep1[y]]];
	if(x == y) return x;
	for(int i=lg[dep1[x]];i>=0;i--) if(f[x][i] != f[y][i])
		x = f[x][i], y = f[y][i];
	return f[x][0];
}

int rd() {
	int ret = 0;
	char c = getchar();
	while(!isdigit(c)) c = getchar();
	while(isdigit(c)) ret = ret * 10 + c - '0', c = getchar();
	return ret;
}

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

void work() {
	n = rd(), m = rd(), q = rd();
	for(int i=2;i<=n;i++) lg[i] = lg[i>>1] + 1;
	int x, y, w;
	for(int i=1;i<=m;i++) x = rd(), red[x] = 1;
	for(int i=1;i<n;i++) x = rd(), y = rd(), w = rd(), push(x, y, w);
	dfs(1, 0, 0);
	// for(int i=1;i<=n;i++) printf("dp[%d] = %lld\n", i, dp[i]);
	vector<int> v;
	// puts("------");
	for(int i=1;i<=q;i++) {
		v.clear();
		scanf("%d", &k);
		for(int j=1;j<=k;j++) cin>>x, v.push_back(x), vis[x] = 1;
		sort(v.begin(), v.end(), cmp);
		v.push_back(1);
		ll ans = 0x3f3f3f3f3f3f3f3f;
		int l = v[0];
		ll mx = dep[v[0]];
		for(int j=0;j<k;j++) {
			ans = min(ans, max(mx - dep[l], dp[v[j+1]])); 
			l = lca(l, v[j+1]);
			mx = max(mx, dep[v[j+1]]);
		}
		printf("%lld\n", ans);
		for(auto x : v) vis[x] = 0;
		// if(T != 2) cout << k << ' ';
		// if(T != 2) for(int j=1;j<=k;j++) cout << v[j] << ' ';
		// if(T != 2) puts("");
	}
	for(int i=1;i<=n;i++) e[i].clear(), red[i] = 0;
	tot = 0;
	// if(T != 2) {
	// 	int res = (sizeof(e) + sizeof(vt::e) + sizeof(f)) / 1024 / 1024;
	// 	if(res != 12) cout << t << '\n', cout << res << '#\n';
	// }
}
int main(){
	// cout << sizeof(f) / 1024 / 1024 << '\n';
// ios::sync_with_stdio(false), cin.tie(0);
	cin>>t; T = t;
	for(int i=1;i<=t;i++) work();
	return 0;
}