//#pragma GCC optimize(3,"Ofast","inline")
//#pragma GCC optimize(2)
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pll;
int main(){
    ios::sync_with_stdio(0); cin.tie(0);
	int T=1;
	cin>>T;
	while(T--){
		ll n,m,q;
		cin>>n>>m>>q;
		vector<ll>color(n+5),dis(n+5,1e16),dep(n+5),des(n+5);
		for(int i=1;i<=m;i++){
			int r; cin>>r;
			color[r]=1;
			dis[r]=0;
		}
		vector<vector<pll>>ed(n+5);
		vector<vector<ll>>fa(n+5,vector<ll>(20));
		for(int i=1;i<n;i++){
			int u,v,w;
			cin>>u>>v>>w;
			ed[u].push_back({v,w});
			ed[v].push_back({u,w});
		}
		function<void(ll)>dfs1=[&](int u){
			for(int i=1;i<=19;i++)
				fa[u][i]=fa[fa[u][i-1]][i-1];
			for(auto [v,w]:ed[u]){
				if(v==fa[u][0])
					continue;
				fa[v][0]=u,dep[v]=dep[u]+1,des[v]=des[u]+w;
				dfs1(v);
			}
		};
		auto lca=[&](int u,int v)->ll
		{
			if(dep[u]<dep[v])
				swap(u,v);
			for(int i=19;i>=0;i--)
				if(dep[fa[u][i]]>=dep[v])
					u=fa[u][i];
			if(u==v)
				return u;
			for(int i=19;i>=0;i--){
				if(fa[u][i]!=fa[v][i])
					u=fa[u][i],v=fa[v][i];
			}
			return fa[u][0];
		};
		auto dist=[&](int u,int v)->ll
		{
			return des[u]+des[v]-2*des[lca(u,v)];
		};
		fa[1][0]=0;
		dfs1(1);
		function<void(ll fa,ll u,ll now)>dfs=[&](ll fa,ll u,ll now)
		{
			if(color[u]==1){
				now=0;
			}
			dis[u]=now;
			for(auto [v,w]:ed[u]){
				if(v==fa)
					continue;
				dfs(u,v,now+w);
			}
		};
		dfs(0,1,0);
		
		while(q--){
			ll k;
			cin>>k;
			vector<ll>v(k+5);
			vector<pll>val(k+5);
			for(int i=1;i<=k;i++){
				cin>>v[i];
				val[i]={dis[v[i]],v[i]};
			}
			
			sort(val.begin()+1,val.begin()+1+k,[&](pll x,pll y){
				return x.first>y.first;
			});
			auto check=[&](ll x)->bool
			{
				int p=val[1].second;
				//cout<<x<<" "<<p<<"\n";
				for(int i=2;i<=k;i++){
					if(val[i].first<=x){
						break;
					}
					//cout<<val[i].second<<" "<<p<<"\n";
					p=lca(p,val[i].second);
				}
				//cout<<"\n";
				for(int i=2;i<=k;i++){
					if(val[i].first<=x){
						break;
					}
					if(dist(val[i].second,p)>x){
						return 0;
					}
				}
				return 1;
				
			};
			//vector<ll>vis(k+5);
			ll l=0,r=val[1].first;
			while(l<=r){
				ll mid=(l+r)>>1;
				if(check(mid)){
					r=mid-1;
				}
				else{
					l=mid+1;
				}
			}
			cout<<l<<"\n";
		}
	}
}
/*

2
12 2 4
1 9
1 2 1
2 3 4
3 4 3
3 5 2
2 6 2
6 7 1
6 8 2
2 9 5
9 10 2
9 11 3
1 12 10
3 3 7 8
4 4 5 7 8
4 7 8 10 11
3 4 5 12
3 2 3
1 2
1 2 1
1 3 1
1 1
2 1 2
3 1 2 3
*/