#include <iostream>
#include <vector>
#include <tuple>
#include <algorithm>
#include <cassert>
#include <cmath>
using namespace std;
#define int long long
const int inf = 1e18;
using i2 = pair<int, int>;
using i3 = tuple<int, int, int>;
const int N = 1e5 + 1;
const int K = 20;
int n, m, q, T, d[N], D[N], I[N], O[2 * N], E[N], st[2 * N][K];
bool r[N];
vector<i2> G[N];
void dfs(int x, int p) {
    O[E[x] = I[x] = T++] = x;
    d[x] = d[p] + 1;
    for (auto [y, w] : G[x]) if (y != p) {
        D[y] = !r[y] * (D[x] + w);
        dfs(y, x);
        O[I[x] = T++] = x;
    }
}
int mn(int x, int y) { return d[x] < d[y] ? x : y; }
int upd(int& x, int y) { return x = mn(x, y); }
int lg(int i) {
    return i ? __builtin_clzll(1) - __builtin_clzll(i) : -1;
}
int lca(int u, int v) {
    int l = I[u], r = I[v];
    if (l > r) swap(l, r);
    int k = lg(r - l + 1);
    return mn(st[l][k], st[r - (1 << k) + 1][k]);
}
bool ck(vector<int>& q, int k) {
    int L = 0;
    for (int x : q) if (D[x] > k) {
        L = L ? lca(L, x) : x;
    }
    if (L) {
        for (int x : q) if (D[x] > k) {
            assert(E[L] <= I[x] <= I[L]);
            if (D[x] < D[L] || D[x] - D[L] > k) return false;
        }
    }
    return true;
}
signed main() {
    assert(false);
    cin.tie(0)->sync_with_stdio(0);
    int t;
    cin >> t;
    while (t--) {
        T = 0;
        cin >> n >> m >> q;
        for (int i = 1; i <= n; i++) {
            G[i].clear();
            r[i] = false;
        }
        for (int i = 0; i < m; i++) {
            int x; cin >> x;
            r[x] = true;
        }
        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);
        for (int i = 0; i < m; i++) assert(D[r[i]] == 0);
        assert(T == 2 * n - 1);
        for (int i = 0; i < T; i++) st[i][0] = O[i];
        for (int k = 1; k < K; k++) {
            for (int i = 0; i + (1 << k) <= T; i++) {
                st[i][k] = mn(st[i][k - 1], st[i + (1 << (k - 1))][k - 1]);
                // if (int j = i + (1 << (k - 1)); j < T) upd(st[i][k], st[j][k - 1]);
            }
        }
        for (int i = 1; i <= n; i++) assert(lca(1, i) == 1);
        while (q--) {
            int k; cin >> k;
            vector<int> v(k);
            for (int& x : v) cin >> x;
            int x = 1e14;
            for (int d = x; d > 0; d /= 2) {
                while (x - d >= 0 && ck(v, x - d)) x -= d;
            }
            cout << x << endl;
        }
        // for (int i = 0; i < T; i++) cout << O[i] << " ";
    }
    return 0;
}