#include<bits/stdc++.h>
using namespace std;
using ll=long long;
const int N=1e5+10;
const ll INF=1e18;
int T,n,m,q,col[N],f[N];
ll dis[N];
vector<pair<int,int> >to[N];
namespace Path{
	int dep[N],fa[N],top[N],son[N],siz[N];
	#define v e.first
	#define w e.second
	void dfs1(int u){
		if(col[u])f[u]=u;
		else f[u]=f[fa[u]];
		dep[u]=dep[fa[u]]+1,siz[u]=1;
		son[u]=0;
		for(auto e:to[u])if(v^fa[u]){
			dis[v]=dis[u]+w;
			fa[v]=u,dfs1(v);
			siz[u]+=siz[v];
			if(siz[v]>siz[son[u]])son[u]=v;
		}
	}
	void dfs2(int u,int t){
		top[u]=t;
		if(son[u])dfs2(son[u],t);
		for(auto e:to[u])if(v^fa[u]&&v^son[u])dfs2(v,v);
	}
	#undef v
	#undef w
	void init(){
		dfs1(1),dfs2(1,1);
	}
	int LCA(int u,int v){
//		cerr<<u<<' '<<v<<endl;
		for(;top[u]^top[v];u=fa[top[u]]){
			if(dep[top[u]]<dep[top[v]])swap(u,v);
		}
		return dep[u]<dep[v]?u:v;
	}
}
using Path::LCA;
void get(){
	scanf("%d%d%d",&n,&m,&q);
	for(int i=1,x;i<=m;i++){
		scanf("%d",&x),col[x]=1;
	}
	for(int i=1,u,v,w;i<n;i++){
		scanf("%d%d%d",&u,&v,&w);
		to[u].push_back({v,w}),to[v].push_back({u,w});
	}
	Path::init();
	for(int t;q--;){
		scanf("%d",&t);
		vector<int>a(t);
		for(int i=0;i<t;i++)scanf("%d",&a[i]);
		auto chk=[&](ll mid){
			vector<int>p;
			for(int i=0;i<t;i++){
				if(dis[a[i]]-dis[f[a[i]]]>mid){
					p.push_back(a[i]);
				}
			}
			if(p.empty())return 1;
			int x=p[0];
			for(int i=1;i<p.size();i++)x=LCA(x,p[i]);
			for(int i:p)if(dis[i]-dis[x]>mid)return 0;
			return 1;
		};
		ll l=-1,r=INF,mid;
		for(;l+1<r;){
			mid=(l+r)>>1;
			if(chk(mid))r=mid;
			else l=mid;
		}
		printf("%lld\n",r);
	}
}
void clr(){
	for(int i=1;i<=n;i++){
		col[i]=0;
		to[i].clear();
	}
}
int main(){
	for(scanf("%d",&T);T--;clr())get();
	return 0;
}