#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;
const ll N=2e5+5;
vector<int>dfn,pos,mp;
vector<int>vec[N];
void DFS(int u,int pre)
{
    dfn.push_back(u);
    pos[u]=dfn.size()-1;
    mp[dfn.size()-1]=u;
    for(auto v:vec[u])if(v!=pre)
    {
        DFS(v,u);
        dfn.push_back(u);
    }
}
template <typename T>
class SparseTable
{
  using VT = vector<T>;
  using VVT = vector<VT>;
  using func_type = function<T(const T &, const T &)>;

  VT V;
  VVT ST;

  static T default_func(const T &t1, const T &t2) { return min(t1, t2); }

  func_type op;

 public:
  SparseTable(const vector<T> &v, func_type _func = default_func) {
    V = v;
    op = _func;
    int len = v.size(), l1 = ceil(log2(len)) + 1;
    ST.assign(len, VT(l1, 0));
    for (int i = 0; i < len; ++i) {
      ST[i][0] = v[i];
    }
    for (int j = 1; j < l1; ++j) {
      int pj = (1 << (j - 1));
      for (int i = 0; i + pj < len; ++i) {
        ST[i][j] = op(ST[i][j - 1], ST[i + (1 << (j - 1))][j - 1]);
      }
    }
  }

  T query(int l, int r) {
    if (l == r)return V[l];
    int lt = r - l + 1;
    int q = ceil(log2(lt)) - 1;
    return op(ST[l][q], ST[r - (1 << q) + 1][q]);
  }
};
int LCA(int x,int y,SparseTable<int>& st)
{
    --x,--y;
    x=pos[x],y=pos[y];
    if(x==y)return mp[x]+1;
    return mp[st.query(min(x,y),max(x,y))]+1;
}
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;
		dfn.clear();
		pos.clear();
		mp.clear();
		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;
		}
		for(int i=0;i<=n;++i)vec[i].clear();
		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});
			--u,--v;
			vec[u].push_back(v);
			vec[v].push_back(u);
		}
        pos.resize(n);
        mp.resize(2*n);
        DFS(0,-1);
        for(auto &x:dfn)x=pos[x];
        SparseTable<int> st(dfn);
		function<void(ll)>dfs1=[&](int u){
			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 dist=[&](int u,int v)->ll
		{
		    //cout<<LCA(u,v,st)<<endl;
		    //cout<<u<<" "<<v<<endl;
			return des[u]+des[v]-2*des[LCA(u,v,st)];
		};
		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,st);
					//cout<<"p="<<p<<endl;
				}
				//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";
		}
	}
}