#include <bits/stdc++.h>
using namespace std;

typedef long long ll; typedef unsigned long long ull;
const int inf = 1e9; const ll llnf = 4e18;

template< class Tp > void chkmax( Tp &x , Tp y ) { x = max( x , y ); }
template< class Tp > void chkmin( Tp &x , Tp y ) { x = min( x , y ); }

void solve( ) {
	int n , m , q; cin >> n >> m >> q;
	vector< int > a( n + 1 ); for( int i = 1; i <= m; i ++ ) { int u; cin >> u; a[u] = true; }
	vector< vector< pair< int , int > > > G( n + 1 ); for( int i = 1; i < n; i ++ ) { int u , v , w; cin >> u >> v >> w; G[u].emplace_back( v , w ) , G[v].emplace_back( u , w ); }

	vector< vector< int > > anc( n + 1 , vector< int >( __lg( n ) + 1 ) ); vector< int > dep( n + 1 );
	vector< ll > weight( n + 1 ) , sum( n + 1 );
	auto dfs = [&] ( auto dfs , int u , int fa ) -> void {
		dep[u] = dep[fa] + 1; for( int k = 0; k <= __lg( n ); k ++ ) anc[u][k] = ( !k ) ? ( fa ) : ( anc[anc[u][k - 1]][k - 1] );
		for( auto [ v , w ] : G[u] ) if( v != fa ) weight[v] = a[v] ? 0 : weight[u] + w , sum[v] = sum[u] + w , dfs( dfs , v , u );
	} ; dfs( dfs , 1 , 0 );

	auto lca = [&] ( int u , int v ) -> int {
		if( dep[u] > dep[v] ) swap( u , v );
		for( int k = __lg( n ); k >= 0; k -- ) if( dep[u] <= dep[anc[v][k]] ) v = anc[v][k];
		for( int k = __lg( n ); k >= 0; k -- ) if( anc[u][k] != anc[v][k] ) u = anc[u][k] , v = anc[v][k];
		while( u != v ) u = anc[u][0] , v = anc[v][0]; return u;
	} ;

	while( q -- ) {
		int k; cin >> k; vector< int > S; while( k -- ) { int u; cin >> u; S.emplace_back( u ); }

		auto check = [&] ( ll x ) -> bool {
			int lc = 0; for( int u : S ) if( weight[u] > x ) lc = ( !lc ? u : lca( lc , u ) );
			if( !lc ) return true;
			else { for( int u : S ) if( sum[u] - sum[lc] > x && weight[u] > x ) return false; return true; }
		} ;

		ll lef = 0 , rig = 1e14 , ans = llnf;
		while( lef <= rig ) { ll mid = ( lef + rig ) / 2; ( check( mid ) ) ? ( rig = mid - 1 , ans = mid ) : ( lef = mid + 1 ); }
		cout << ans << "\n";
	}
}

int main( ) {
	ios::sync_with_stdio( 0 ), cin.tie( 0 ), cout.tie( 0 );
	int T; cin >> T; while( T -- ) solve( ); return 0;
}