#include <bits/stdc++.h>
#define ll long long
#define fi first
#define se second
#define endl '\n'
#define MASK(i) (1LL << (i))
#define ull unsigned long long
#define ld long double
#define pb push_back
#define all(x) (x).begin() , (x).end()
#define BIT(x , i) ((x >> (i)) & 1)
#define TASK "task"
#define sz(s) (int) (s).size()
 
using namespace std;
const int mxN = 5e5 + 227;
const int inf = 1e9 + 277;
const int mod = 1e9 + 7;
const ll infll = 1e15 + 7;
const int base = 307;
const int LOG = 20;
 
template <typename T1, typename T2> bool minimize(T1 &a, T2 b) {
    if (a > b) {a = b; return true;} return false;
}
template <typename T1, typename T2> bool maximize(T1 &a, T2 b) {
    if (a < b) {a = b; return true;} return false;
}
 
int n;
int m;
int q;
int a[mxN];
int dep[mxN];
int par[mxN][LOG + 1];
bool red[mxN];
ll dist[mxN];
pair<ll, int> best[mxN];
vector<pair<int, int>> adj[mxN];
int timer = 0;

void dfs(int u, int p, int cur = -1) {
    if(red[u] == true) cur = u;
    for(auto it : adj[u]) {
        int v = it.fi;
        int c = it.se;
        if(v == p) continue;
        dist[v] = dist[u] + c;
        dep[v] = dep[u] + 1;
        par[v][0] = u;
        dfs(v, u, cur);
    }

    best[u] = make_pair(dist[u] - dist[cur], cur);
}


int getlca(int u, int v) {
    if(dep[u] < dep[v]) swap(u, v);
    for(int j = LOG; j >= 0; j--) if(dep[par[u][j]] >= dep[v]) u = par[u][j];
    if(u == v) return u;
    for(int j = LOG; j >= 0; j--) {
        if(par[u][j] != par[v][j]) {
            u = par[u][j];
            v = par[v][j];
        }
    }
    return par[u][0];
}

bool cmp(int x, int y) {
    return best[x].fi >= best[y].fi;
}
 
void solve()
{
    cin >> n >> m >> q;
    for(int i = 1; i <= m; i++) {
        int x; cin >> x;
        red[x] = true;
    }
    for(int i = 1; i < n; i++) {
        int u, v, c;
        cin >> u >> v >> c;
        adj[u].pb({v, c});
        adj[v].pb({u, c});
    }

    par[1][0] = 1;
    dfs(1, -1);
 
    for (int j = 1; j <= LOG; j++)
    for (int i = 1; i <= n; i++) par[i][j] = par[par[i][j - 1]][j - 1];

    while(q--) {
        int k; cin >> k;
        ll res = -infll;
        vector<int> node;
        for(int i = 1; i <= k; i++) {
            int x; cin >> x;
            node.pb(x);
            maximize(res, best[x].fi);
        }

        sort(all(node), cmp);

        int lca = node[0];
        ll maxDist = dist[node[0]];
        for(int i = 0; i < sz(node); i++) {
            lca = getlca(lca, node[i]);
            maximize(maxDist, dist[node[i]]);
            if(i + 1 < sz(node)) minimize(res, max(maxDist - dist[lca], best[node[i + 1]].fi));
            else minimize(res, maxDist - dist[lca]);

        }
        cout << res << endl;
    }
    for(int u = 1; u <= n; u++) {
        adj[u].clear();
        red[u] = false;
    }
}
 
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    // freopen(TASK".inp" , "r" , stdin);
    // freopen(TASK".out" , "w" , stdout);
 
    int tc = 1;
    cin >> tc;
    while(tc--) {
        solve();
    }
    return 0;
}