#include <bits/stdc++.h>
using namespace std;
#define endl "\n"
#define int long long 
void solved(){
    int n,m,q;
    cin>>n>>m>>q;
    vector<vector<int>> fa(n+1,vector<int>(20));
    vector<vector<pair<int,int>>> adj(n+1);
    vector<int> r(m+1),dis(n+1),d1(n+1,2e18),dep(n+1);
    for(int i=1;i<=m;i++) cin>>r[i],d1[r[i]]=0;
    for(int i=1;i<=n-1;i++){
        int a,b,w;
        cin>>a>>b>>w;
        adj[a].push_back({b,w});
        adj[b].push_back({a,w});
    }
    dep[1]=1;
    auto dfs=[&](auto self,int u,int p)->void{
          for(auto &[v,w]:adj[u]){

              if(v==p) continue;
              fa[v][0]=u;
              dep[v]=dep[u]+1;
              for(int i=1;i<=19;i++) fa[v][i]=fa[fa[v][i-1]][i-1];
              dis[v]=dis[u]+w;
              if(d1[v]) d1[v]=d1[u]+w; 
              self(self,v,u);
          }   
    };
    //cout<<1<<endl;
    dfs(dfs,1,0);
    auto lca=[&](int u,int v){
         if(dep[u]<dep[v]) swap(u,v);
         for(int i=19;i>=0;i--){
            if(dep[u]-dep[v]>=(1ll<<i)){
                u=fa[u][i];
            }
         }
         if(u==v) return v;
         for(int i=19;i>=0;i--){
            if(fa[u][i]==fa[v][i]) continue;
            u=fa[u][i];
            v=fa[v][i];
         }
         return fa[v][0];
    };

    while(q--){
        int k;
        cin>>k;
        vector<pair<int,int>> s;
        for(int i=1;i<=k;i++){
            int x;
            cin>>x;
            s.push_back({d1[x],x});
        }
        sort(s.rbegin(),s.rend());
        int bf=s[0].second;
        int ans=s[0].first;
        int d2=0;
        for(int i=0;i<k;i++){
            //cout<<s[i].first<<" "<<s[i].second<<" "<<dis[s[i].second]<<" ";
            bf=lca(bf,s[i].second);
            //cout<<bf<<endl;
            d2=max(d2,dis[s[i].second]);
            ans=min(max(d2-dis[bf],i==k-1?0:d1[s[i+1].second]),ans);
        }
        cout<<ans<<endl;
    }
} 
signed main()
{
   ios::sync_with_stdio(false);
   cin.tie(0);
   cout.tie(0);
   int t=1;
   cin>>t;
   while(t--){
     solved();
   }
}