#include <bits/stdc++.h>
#define int long long 
#define ii pair<int,int>
#define ff first
#define ss second

using namespace std;
const int maxn = 1e5 + 10, init = 0;
vector<ii> adj[maxn];
int in[maxn], dp[maxn], out[maxn], dep[maxn], depth[maxn], mark[maxn];
int p[maxn][20], w[maxn][20], seg[2*maxn];
int n, m, q, k, cnt;

void DFS(int u = 1, int pa = 0, int cur = 0)
{
    if (mark[u]) cur = 0;
    in[u] = ++cnt;
    dp[u] = cur;
    for (auto [v, c]: adj[u]) if (v != pa)
    {
        p[v][0] = u;
        w[v][0] = c;
        dep[v] = dep[u] + 1;
        depth[v] = depth[u] + c;
        DFS(v, u, cur + c);
    }
    out[u] = cnt;
}

inline int lca(int u, int v)
{
    if (dep[u] > dep[v]) swap(u, v);
    int dif = dep[v] - dep[u];
    for (int i=k; i>=0; i--) if (dif >> i & 1) v = p[v][i];
    if (v == u) return u;
    for (int i=k; i>=0; i--) if (p[v][i] != p[u][i]) v = p[v][i], u = p[u][i];
    return p[u][0];
}

inline void upd(int pos, int val)
{
    seg[pos+=n] = val;
    while (pos >>= 1) seg[pos] = max(seg[pos<<1], seg[pos<<1|1]);
}

inline int qry(int l, int r)
{
    int ans = 0;
    for (l+=n, r+=n+1; l<r; l>>=1, r>>=1)
    {
        if (l & 1) ans = max(ans, seg[l++]);
        if (r & 1) ans = max(ans, seg[--r]);
    }
    return ans;
}

signed main()
{
    ios_base::sync_with_stdio(0); cin.tie(0);
    if (fopen("input.in", "r")) {
        freopen("input.in", "r", stdin);
        freopen("output.out", "w", stdout);
    }
    int tst; cin>>tst; while (tst--)
    {
        cin>>n>>m>>q;
        for (int i=1; i<=n; i++) mark[i] = 0, adj[i].clear();
        for (int i=1; i<=(n<<1|1); i++) seg[i] = init;
        for (int i=1, x; i<=m; i++) cin>>x, mark[x] = 1;
        for (int i=1, u, v, c; i<n; i++)
        {
            cin>>u>>v>>c;
            adj[u].emplace_back(v, c);
            adj[v].emplace_back(u, c);
        }
        cnt = 0;
        dep[1] = depth[1] = 0;
        DFS();
        k = log2(n);
        for (int i=1; i<=k; i++)
            for (int j=1; j<=n; j++)
                p[j][i] = p[p[j][i-1]][i-1],
                w[j][i] = w[j][i-1] + w[p[j][i-1]][i-1];
        while (q--)
        {
            vector<int> v, v2;
            int x;
            cin>>x;
            v.resize(x);
            for (int &i: v) cin>>i;
            sort(v.begin(), v.end(), [](int x, int y) {return dp[x] > dp[y];});
            int cur = v[0], ans = dp[v[0]];
            for (int i=1; i<x; i++) 
                if (dp[v[i]] == ans) cur = lca(cur, v[i]);
                else break;
            sort(v.begin(), v.end(), [](int x, int y) {return in[x] < in[y];});
            for (int i: v) v2.emplace_back(in[i]);
            vector<int> pref(x), suf(x);
            pref[0] = dp[v[0]];
            suf[x-1] = dp[v[x-1]];
            for (int i=1; i<x; i++) pref[i] = max(pref[i-1], dp[v[i]]);
            for (int i=x-2; i>=0; i--) suf[i] = max(suf[i+1], dp[v[i]]);
            for (int i: v) upd(in[i], depth[i]);
            // cout<<"ANS: "<<ans<<"\n";
            for (int i: v)
            {
                int tmp = lca(cur, i);
                int le = in[tmp], ri = out[tmp];
                int posl = lower_bound(v2.begin(), v2.end(), le) - v2.begin();
                int posr = upper_bound(v2.begin(), v2.end(), ri) - v2.begin() - 1;
                int prel = (posl > 0 ? pref[posl-1] : 0);
                int sufr = (posr < x - 1 ? suf[posr+1] : 0);
                int mid = qry(le, ri) - depth[tmp];
                ans = min(ans, max({prel, sufr, mid}));
                // cout<<tmp<<" "<<ans<<"\n";
            }
            for (int i: v) upd(in[i], 0);
            cout<<ans<<"\n";
        }
    }
}
/**
 * 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
*/