#include<bits/stdc++.h>
#define int long long
using namespace std;
struct edge{
	int to,nxt,w;
}e[200010];
int T,n,m,q,nE = 0;
int hd[200010];
int col[100010],dis[100010],val[100010],f[100010][20],dep[100010];
void add(int u,int v,int w){
	e[++nE] = (edge){v,hd[u],w};
	hd[u] = nE;
}
void dfs(int u,int fa){
	dep[u] = dep[fa] + 1;
	f[u][0] = fa;
	for(int i = 1; i < 20; i++) f[u][i] = f[f[u][i - 1]][i - 1];
	if(col[u]) val[u] = 0;
	for(int i = hd[u]; i; i = e[i].nxt){
		int v = e[i].to,w = e[i].w;
		if(v == fa) continue;
		dis[v] = dis[u] + w;
		val[v] = val[u] + w;
		dfs(v,u);
	}
}
int LCA(int u,int v){
	if(dep[u] < dep[v]) swap(u,v);
	for(int i = 19; i >= 0; i--) if(dep[f[u][i]] >= dep[v]) u = f[u][i];
	if(u == v) return u;
	for(int i = 19; i >= 0; i--){
		if(f[u][i] != f[v][i]){
			u = f[u][i];
			v = f[v][i];
		}
	}
	return f[u][0];
}
bool cmp(int a,int b){
	return val[a] > val[b];
}
signed main(){
	scanf("%lld",&T);
	while(T--){
		scanf("%lld %lld %lld",&n,&m,&q);
		nE = 0;
		for(int i = 0; i <= n; i++) col[i] = 0,hd[i] = 0;
		for(int i = 1,x; i <= m; i++){
			scanf("%lld",&x);
			col[x] = 1;
		}
		for(int i = 1,u,v,w; i < n; i++){
			scanf("%lld %lld %lld",&u,&v,&w);
			add(u,v,w),add(v,u,w);
		}
		dfs(1,0);
		while(q--){
			vector<int>vc;
			int k;
			scanf("%lld",&k);
			for(int i = 1,x; i <= k; i++) scanf("%lld",&x),vc.push_back(x);
			sort(vc.begin(),vc.end(),cmp);
			vc.push_back(0);
			int lca = vc[0],ans = val[vc[1]],mx = dis[vc[0]];
			for(int i = 1; i < k; i++){
				lca = LCA(lca,vc[i]);
				mx = max(mx,dis[vc[i]]);
				ans = min(ans,max(val[vc[i + 1]],mx - dis[lca]));
			}
			printf("%lld\n",ans);
		}
	}
	return 0;
}