#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pii pair<int, int>
#define inf 0x3f3f3f3f
#define endl '\n'
const int N = 1e5 + 5;
const int mod = 998244353;

int col[N], cost[N];
vector<pii> g[N];
int dep[N], fa[N][22], lg[N], sum[N][22];
void dfs(int now, int fath, int val)
{
    fa[now][0] = fath;
    sum[now][0] = val;
    dep[now] = dep[fath] + 1;
    for (int i = 1; i <= lg[dep[now]]; i++)
    {
        fa[now][i] = fa[fa[now][i - 1]][i - 1];
        sum[now][i] = sum[now][i - 1] + sum[fa[now][i - 1]][i - 1];
    }
    for (auto [v, w] : g[now])
        if (v != fath)
            dfs(v, now, w);
}
void dfs1(int u, int f, int sum)
{
    if (col[u]) sum = 0;
    else cost[u] = sum;
    for (auto [v, w]: g[u])
    {
        if (v == f) continue;
        dfs1(v, u, sum + w);
    }
}
int lca(int x, int y)
{
    if (dep[x] < dep[y]) swap(x, y);
    while (dep[x] > dep[y]) x = fa[x][lg[dep[x] - dep[y]] - 1];
    if (x == y) return x;
    for (int k = lg[dep[x]] - 1; k >= 0; k--)
        if (fa[x][k] != fa[y][k])
            x = fa[x][k], y = fa[y][k];
    return fa[x][0];
}
struct node {
    int i, w;
    bool operator<(const node& p) {
        return w > p.w;
    }
};
void solve()
{
    int n, m, q; cin >> n >> m >> q;
    for (int i = 1; i <= n; i++)
    {
        col[i] = cost[i] = dep[i] = 0;
        g[i].clear();
        for (int j = 0; j <= 21; j++) fa[i][j] = 0;
    }
    for (int i = 1; i <= m; i++) 
    {
        int x; cin >> x;
        col[x] = 1;
    }
    for (int i = 1; i < n; i++)
    {
        int u, v, w; cin >> u >> v >> w;
        g[u].push_back({v, w}), g[v].push_back({u, w});
    }
    dfs(1, 0, 0);
    dfs1(1, 0, 0);
    // for (int i = 1; i <= n; i++) cout << cost[i] << endl;
    while (q--)
    {
        int s; cin >> s;
        vector <node> v;
        for (int i = 1; i <= s; i++)
        {
            int x; cin >> x;
            v.push_back({x, cost[x]});
        }
        if (s == 1) 
        {
            cout << 0 << endl;
            continue;
        }
        sort(v.begin(), v.end());
        int l = v[0].i, ans = v[1].w, maxx = v[0].w;
        for (int i = 1; i < (int)v.size(); i++)
        {
            auto [x, w] = v[i];
            l = lca(l, x);
            maxx = max(maxx, w);
            // cout << l << " " << maxx << endl;
            if(i != (int)v.size() - 1)
                ans = min(ans, max(maxx - cost[l], v[i + 1].w));
            else ans = min(ans, maxx - cost[l]);
        }
        cout << ans << endl;
    }
}
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    for (int i = 1; i < N; i++) lg[i] = lg[i - 1] + (1 << lg[i - 1] == i);
    int T = 1; cin >> T;
    while (T--) solve();
    return 0;
}

/*
2
12 2 4
1 9
1 2 1
2 3 4
3 4 3
3 5 2
2 6 2
6 7 1
6 8 2
2 9 5
9 10 2
9 11 3
1 12 10
3 3 7 8
4 4 5 7 8
4 7 8 10 11
3 4 5 12

3 2 3
1 2
1 2 1
1 3 1 
1 1
2 1 2
3 1 2 3
*/