#include<bits/stdc++.h>

using namespace std;
using lint = int64_t;
const lint linf = 1e18;

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    int t;
    cin>>t;
    while(t--){
        int n, m, q;
        cin>>n>>m>>q;
        vector<int>x(m);
        vector<bool>w(n);
        for(int i=0;i<m;i++) cin>>x[i], x[i]--, w[x[i]] = 1;
        vector<vector<pair<int, int>>>g(n);
        for(int i=1;i<n;i++){
            int a, b, c;
            cin>>a>>b>>c;
            a--, b--;
            g[a].emplace_back(b, c);
            g[b].emplace_back(a, c);
        }
        vector<lint>d(n), dp(n);
        dp[0] = linf;
        vector<int>tin(n), h(n);
        int timer = 0;
        vector<vector<int>>anc(17, vector<int>(n));

        auto dfs = [&](auto& self, int u, int p)->void {
            tin[u] = timer++;
            anc[0][u] = p;
            if(w[u]) dp[u] = 0;
            for(auto [v, c] : g[u]){
                if(v == p) continue;
                h[v] = h[u] + 1;
                d[v] = d[u] + c;
                dp[v] = dp[u] + c;
                self(self, v, u);
            }
        };

        dfs(dfs, 0, 0);
        for(int b=1;b<17;b++){
            for(int i=0;i<n;i++) anc[b][i] = anc[b-1][anc[b-1][i]];
        }

        auto get_lca = [&](int u, int v)->int {
            if(h[u] < h[v]) swap(u, v);
            int c = h[u] - h[v];
            for(int b=16;b>=0;b--) if(c>>b&1) u = anc[b][u];
            for(int b=16;b>=0;b--) if(anc[b][u] != anc[b][v]) u = anc[b][u], v = anc[b][v];
            if(u != v) u = anc[0][u];
            return u;
        };

        while(q--){
            int k;
            cin>>k;
            vector<int>v(k);
            for(int i=0;i<k;i++) cin>>v[i], v[i]--;
            sort(v.begin(), v.end(), [&](int i, int j){
                return tin[i] < tin[j];
            });
            lint lo = 0, hi = 1e16;
            while(lo <= hi){
                lint mid = (lo + hi) >> 1;
                vector<int>cur;
                for(int i : v) if(dp[i] > mid) cur.push_back(i);
                bool ok = true;
                if(!cur.empty()){
                    int lca = get_lca(cur[0], cur.back());
                    for(int i : cur) if(d[i] - d[lca] > mid) ok = false;
                }
                if(ok) hi = mid - 1;
                else lo = mid + 1;
            }
            cout<<lo<<"\n";
        }

    }
    return 0;
}