#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
const int N = 1e5 + 5;
// const int M = 2e7 + 5;
// const int mod = 998244353;
// const int mod = 1000000007;

int n, m, q, fa[N][18], col[N], dep[N], lst[N], dfn[N], dfs_tot;
i64 dis[N];
vector<pair<int, int>> adj[N];
void dfs1(int cur, int f)
{
    dfn[cur] = ++dfs_tot;
    dep[cur] = dep[f] + 1;
    if (col[cur])
        lst[cur] = cur;
    for (auto [i, val] : adj[cur])
    {
        if (i == f)
            continue;
        fa[i][0] = cur, lst[i] = lst[cur];
        for (int j = 1; j <= 17; j++)
            fa[i][j] = fa[fa[i][j - 1]][j - 1];
        dis[i] = dis[cur] + val;
        dfs1(i, cur);
    }
}
int findlca(int x, int y)
{
    if (x == y)
        return x;
    if (dep[x] < dep[y])
        swap(x, y);
    for (int i = 17; i >= 0; i--)
        if (dep[fa[x][i]] >= dep[y])
            x = fa[x][i];
    if (x == y)
        return x;
    for (int i = 17; i >= 0; i--)
        if (fa[x][i] != fa[y][i])
            tie(x, y) = tie(fa[x][i], fa[y][i]);
    return fa[x][0];
}

bool flag[N];
vector<int> G[N];
int k, h[N], sta[N], top;
i64 ans, mxval[N], mxdep[N], rval[N];
void dfs2(int cur)
{
    mxdep[cur] = mxval[cur] = rval[cur] = 0;
    if (flag[cur] && !col[cur])
        mxdep[cur] = dis[cur], mxval[cur] = dis[cur] - dis[lst[cur]];
    for (int i : G[cur])
    {
        dfs2(i);
        if (!col[cur] && !col[i] && lst[i] == lst[cur])
        {
            mxdep[cur] = max(mxdep[i], mxdep[cur]);
            mxval[cur] = max(mxval[i], mxval[cur]);
            rval[cur] = max(rval[cur], rval[i]);
        }
        else
        {
            mxval[cur] = max(mxval[i], mxval[cur]);
            rval[cur] = max(rval[cur], mxval[i]);
        }
    }
}
void dfs3(int cur, i64 val)
{
    ans = min(ans, max({val, mxdep[cur] - dis[cur], rval[cur]}));
    if (flag[cur] && !col[cur])
        val = max(val, dis[cur] - dis[lst[cur]]);
    int siz = G[cur].size();
    vector<i64> pre(siz + 2), suf = pre;
    for (int j = 0; j < siz; j++)
        pre[j + 1] = max(pre[j], mxval[G[cur][j]]);
    for (int j = siz - 1; j >= 0; j--)
        suf[j + 1] = max(suf[j + 2], mxval[G[cur][j]]);
    for (int j = 0; j < siz; j++)
    {
        int i = G[cur][j];
        dfs3(i, max({val, pre[j], suf[j + 2]}));
    }
}
void solve()
{
    cin >> n >> m >> q;
    for (int i = 1, x; i <= m; i++)
    {
        cin >> x;
        col[x] = 1;
    }
    for (int i = 1, u, v, w; i < n; i++)
    {
        cin >> u >> v >> w;
        adj[u].push_back({v, w});
        adj[v].push_back({u, w});
    }
    dfs1(1, 0);
    while (q--)
    {
        cin >> k;
        for (int j = 1; j <= k; j++)
        {
            cin >> h[j], flag[h[j]] = 1;
            if (!col[h[j]])
                ans = max(ans, dis[h[j]] - dis[lst[h[j]]]);
        }
        sort(h + 1, h + k + 1, [&](int a, int b)
             { return dfn[a] < dfn[b]; });
        sta[top = 1] = 1;
        G[1].clear();
        for (int i = 1; i <= k; i++)
        {
            if (h[i] == 1)
                continue;
            int f = findlca(h[i], sta[top]);
            if (f != sta[top])
            {
                while (dfn[f] < dfn[sta[top - 1]])
                {
                    G[sta[top - 1]].push_back(sta[top]);
                    top--;
                }
                if (dfn[f] > dfn[sta[top - 1]])
                {
                    G[f].clear();
                    G[f].push_back(sta[top]);
                    sta[top] = f;
                }
                else
                {
                    G[f].push_back(sta[top]);
                    top--;
                }
            }
            sta[++top] = h[i];
            G[h[i]].clear();
        }
        for (int i = 1; i < top; i++)
            G[sta[i]].push_back(sta[i + 1]);
        dfs2(1);
        dfs3(1, 0);
        cout << ans << '\n';
        ans = 0;
        for (int i = 1; i <= k; i++)
            flag[h[i]] = 0;
    }
    dfs_tot = 0;
    for (int i = 1; i <= n; i++)
        adj[i].clear(), col[i] = 0;
}
signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int t = 1;
    cin >> t;
    while (t--)
        solve();
}