#include<bits/stdc++.h>
#ifdef LOCAL
#include "Essentials/algo/debug.h"
#else
#define debug(...)    69
#define debugArr(...)  69
#endif
using namespace std;

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

const int N =1e5 + 23;
const int LOG = 20;
const ll inf = 1e18;

#define F           first
#define S           second
#define pb          push_back
#define kill(x)     cout<<x<<endl, exit(0);
#define all(x)      x.begin(),x.end()
#define sz(x)       (int)x.size()
//#define lc          (v << 1)
#define rc          ((v<<1) |1)
#define int         ll

int n,m,q;
vector<pll> G[N];
int h[N],d[N],up[LOG][N],val[N];
bool is[N];
int qu[N],lc[N],mx[N];

void dfs(int v,int p= 1) {
	if(is[v]) val[v] =0;
	else      val[v] = d[v] - d[p] + val[p];
	up[0][v] = p;
	for(int i = 1; i < LOG; i ++) up[i][v] = up[i-1][up[i-1][v]];
	for(auto [u,w] : G[v]) if(u != p) {
		h[u] = h[v]+ 1;
		d[u] = d[v] + w;
		dfs(u,v);
	}
}

int getP(int v,int k) {
	for(int i = 0 ; i< LOG; i ++) if((k>>i)&1) v= up[i][v];
	return v;
}

int lca(int v,int u) {
	if(min(v,u) == 0) return max(v,u);
	if(h[v] < h[u]) swap(v,u);
	v = getP(v,h[v] - h[u]);
	if(v == u) return v;
	for(int i = LOG-1; i>= 0; i--) if(up[i][v] != up[i][u]) v = up[i][v],u = up[i][u];
	return up[0][v];
}

void solve() {
	cin>>n>>m>>q;
	for(int i = 1; i <= n ; i ++) {
		G[i].clear();
		is[i] = 0;
	}
	for(int i = 0; i < m ; i++) {
		int x; cin>>x;
		is[x] = true;	
	}
	for(int i =1;i <n ; i ++) {
		int v,u,w; cin>>v>>u>>w;
		G[v].pb({u,w}); G[u].pb({v,w});
	}
	dfs(1);
	while(q--) {
		cin>>m;
		fill(qu,qu+m+10,0);
		for(int i = 1; i<= m ; i++) cin>>qu[i];
		sort(qu+1,qu+m+1,[&](int x,int y) {return val[x] > val[y];});
		int ans = val[qu[1]];
		for(int i = 1; i<= m ;i ++) {
			lc[i] = lca(qu[i],lc[i-1]);
			mx[i] = max(mx[i-1],d[qu[i]]);
			ans = min(ans,max(mx[i] - d[lc[i]],val[qu[i+1]]));
		}
		cout<<ans << '\n';
	}
}

int32_t main() {
    cin.tie(nullptr)->sync_with_stdio(false);
	int testcase= 1;
	cin>>testcase;
	for(int tcase = 1; tcase <= testcase; tcase ++) {
		#ifdef LOCAL
			cout<<"\n------------------\n" << "Test case: " <<  tcase<< endl;
		#endif
		solve();
		#ifdef LOCAL
			cout<<endl;
		#endif
	}
    return 0;
}

// Jumpsuit, Jumpsuit cover me!
// Jumpsuit, Jumpsuit cover me!