#include<bits/stdc++.h>
using namespace std ;
typedef long long ll ;
typedef unsigned long long ull ;
typedef pair < int , int > pii ;
typedef vector < int > vi ;
#define fi first
#define se second
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());

#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()

const int MAXN = 1e5 + 7 ;
const int LOG = 18 ;
const ll inf = 1e18 ;

int n , m , q ;
vector < pii > v[ MAXN ] ;
bool spec[ MAXN ] ;
int st[ MAXN ] , en[ MAXN ] , tp ;
ll pref[ MAXN ] ;
int lvl[ MAXN ] , LCA[ MAXN ][ LOG ] ;
int anc[ MAXN ] ;

void dfs ( int x , int prv , int lst ) {
    st[ x ] = ++ tp ;
    anc[ x ] = lst ;
    for ( int i = 1 ; i < LOG ; ++ i ) {
        LCA[ x ][ i ] = LCA[ LCA[ x ][ i - 1 ] ][ i - 1 ] ;
    }
    for ( auto [ y , len ] : v[ x ] ) {
        if ( y == prv ) { continue ; }
        pref[ y ] = pref[ x ] + len ; 
        lvl[ y ] = lvl[ x ] + 1 ;
        LCA[ y ][ 0 ] = x ;
        if ( spec[ y ] == true ) { dfs ( y , x , y ) ; }
        else { dfs ( y , x , lst ) ; }
    }
    en[ x ] = tp ;
}

int get_lca ( int x , int y ) {
    for ( int i = LOG - 1 ; i >= 0 ; -- i ) {
        if ( lvl[ x ] - ( 1 << i ) >= lvl[ y ] ) {
            x = LCA[ x ][ i ] ;
        }
        if ( lvl[ y ] - ( 1 << i ) >= lvl[ x ] ) {
            y = LCA[ y ][ i ] ;
        }
    }
    for ( int i = LOG - 1 ; i >= 0 ; -- i ) {
        if ( LCA[ x ][ i ] != LCA[ y ][ i ] ) {
            x = LCA[ x ][ i ] , y = LCA[ y ][ i ] ;
        }
    }
    if ( x != y ) { x = LCA[ x ][ 0 ] ; }
    return x ;
}

int k ;
int vals[ MAXN ] ;
pair < ll , int > srt[ MAXN ] ;

void solve ( ) {
    cin >> n >> m >> q ;
    for ( int i = 1 ; i <= n ; ++ i ) {
        v[ i ].clear ( ) ;
        spec[ i ] = false ;
    }
    for ( int i = 1 , x ; i <= m ; ++ i ) {
        cin >> x ;
        spec[ x ] = true ;
    }
    for ( int i = 1 , x , y , z ; i < n ; ++ i ) {
        cin >> x >> y >> z ;
        v[ x ].push_back ( { y , z } ) ;
        v[ y ].push_back ( { x , z } ) ;
    }
    tp = 0 ; 
    dfs ( 1 , -1 , 1 ) ;
    while ( q -- ) {
        cin >> k ;
        map < ll , int > aux ;
        for ( int i = 1 ; i <= k ; ++ i ) {
            cin >> vals[ i ] ;
            srt[ i ] = { pref[ vals[ i ] ] - pref[ anc[ vals[ i ] ] ] , vals[ i ] } ;
        }
        sort ( srt + 1 , srt + k + 1 , greater < pair < ll , int > > ( ) ) ;
        int rt = -1 ;
        ll mx = -1 ;
        ll ans = inf ;
        for ( int i = 1 ; i <= k ; ++ i ) {
            if ( rt == -1 ) { rt = srt[ i ].se ; }
            else { rt = get_lca ( rt , srt[ i ].se ) ; }
            mx = max ( mx , pref[ srt[ i ].se ] ) ;
            ll cand = mx - pref[ rt ] ;
            if ( i < k ) { cand = max ( cand , srt[ i + 1 ].fi ) ; }
            ans = min ( ans , cand ) ;
        }
        cout << ans << "\n" ;
    }
}

int main ( ) {
    ios_base :: sync_with_stdio ( false ) ;
    cin.tie ( NULL ) ;
    int t = 1 ; cin >> t ; 
    while ( t -- ) { solve ( ) ; }
    return 0 ;
}