#include <bits/stdc++.h>

using namespace std;

typedef long long int	ll;
typedef pair<int, int>	pii;
typedef pair<ll, ll>	pll;


#define F		        first
#define S		        second
#define pb		        push_back
#define endl            '\n'
#define Mp              make_pair
#define all(x)          x.begin(), x.end()
#define debug(x)        cerr << #x << " = " << x << endl;
#define fast_io         ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define file_io         freopen("tests.in" , "r" , stdin) ;

ll mod = 1e9+7;

const int N = 1e5+23, L=23;

vector<pll> g[N];
int par[N][L], h[N];
ll cost[N], d[N];
int is[N];
int n, m, q;

void dfs(int v, int p=0){
    if(is[v]) cost[v]=0;
    for (auto pp: g[v]){
        int u=pp.F, w=pp.S;
        if(u==p) continue;
        par[u][0]=v;
        h[u]=h[v]+1;
        cost[u]=cost[v]+w;
        d[u]=d[v]+w;
        dfs(u, v);
    }
}

int LCA(int v, int u){
    if(h[v]>h[u]) swap(u, v);
    int d=h[u]-h[v];
    for (int i=0; i<L; i++) if(d>>i&1) u=par[u][i];
    if(v==u) return v;
    for (int i=L-1; i>=0; i--)if(par[u][i]!=par[v][i]){
        v=par[v][i];
        u=par[u][i];
    }
    return par[u][0];
}

void C(){
    for (int i=0; i<=n; i++){
        g[i].clear();
        h[i]=0;
        is[i]=0;
        cost[i]=0;
        d[i]=0;
        for (int j=0; j<L; j++) par[i][j]=0;
    }
}

int main()
{
    fast_io
    int T; cin>>T;
    while(T--){

        cin>>n>>m>>q;
        for (int i=0; i<m; i++){
            int v; cin>>v;
            is[v]=1;
        }
        for (int i=0; i<n-1; i++){
            int v, u, w; cin>>v>>u>>w;
            g[v].pb({u, w}); g[u].pb({v, w});
        }
        dfs(1);
        for (int j=1; j<L; j++)for(int i=1; i<=n; i++) par[i][j]=par[par[i][j-1]][j-1];
        while(q--){
            int k; cin>>k;
            vector<pll> vec;
            for (int i=0; i<k; i++){
                int v; cin>>v;
                vec.pb({cost[v], v});
            }
            if(k==1){ cout<<0<<endl; continue; }
            sort(all(vec)); reverse(all(vec)); vec.pb({0, 0});
            ll ans=vec[1].F, Mxd=d[vec[0].S], u=vec[0].S;
            for (int i=1; i<k; i++){
                u=LCA(u, vec[i].S);
                Mxd=max(Mxd, d[vec[i].S]);
                ans=min(ans, max(vec[i+1].F, Mxd-d[u]));
            }

            cout<<ans<<endl;
        }
        C();
    }

}