#include <bits/stdc++.h>

using i64 = long long;

void solve() {
    int n, m, q;
    std::cin >> n >> m >> q;
    
    std::vector<i64> c(n, 1E18);
    for (int i = 0; i < m; i++) {
        int x;
        std::cin >> x;
        x--;
        c[x] = 0;
    }
    
    std::vector<i64> dep(n);
    std::vector<int> in(n);
    std::vector<std::vector<std::pair<int, int>>> adj(n);
    for (int i = 1; i < n; i++) {
        int u, v, w;
        std::cin >> u >> v >> w;
        u--, v--;
        adj[u].emplace_back(v, w);
        adj[v].emplace_back(u, w);
    }
    std::vector<int> parent(n);
    parent[0] = -1;
    int cur = 0;
    
    const int logn = std::__lg(n);
    std::vector a(logn + 1, std::vector<int>(n - 1));
    auto dfs = [&](auto self, int x) -> void {
        in[x] = cur++;
        if (cur > 1) {
            a[0][cur - 2] = parent[x];
        }
        for (auto [y, w] : adj[x]) {
            if (y == parent[x]) {
                continue;
            }
            parent[y] = x;
            dep[y] = dep[x] + w;
            c[y] = std::min(c[y], c[x] + w);
            self(self, y);
        }
    };
    dfs(dfs, 0);
    
    for (int j = 0; j < logn; j++) {
        for (int i = 0; i + (2 << j) <= n - 1; i++) {
            a[j + 1][i] = dep[a[j][i]] < dep[a[j][i + (1 << j)]] ? a[j][i] : a[j][i + (1 << j)];
        }
    }
    auto lca = [&](int x, int y) {
        if (x == y) {
            return x;
        }
        if (in[x] > in[y]) {
            std::swap(x, y);
        }
        int k = std::__lg(in[y] - in[x]);
        int u = a[k][in[x]];
        int v = a[k][in[y] - (1 << k)];
        return dep[u] < dep[v] ? u : v;
    };
    
    for (int _ = 0; _ < q; _++) {
        int k;
        std::cin >> k;
        
        std::vector<int> v(k);
        for (int i = 0; i < k; i++) {
            std::cin >> v[i];
            v[i]--;
        }
        std::sort(v.begin(), v.end(),
            [&](int i, int j) {
                return c[i] < c[j];
            });
        i64 ans = c[v[k - 1]];
        int l = v[k - 1];
        i64 maxdep = dep[v[k - 1]];
        for (int i = k - 1; i >= 0; i--) {
            maxdep = std::max(maxdep, dep[v[i]]);
            l = lca(l, v[i]);
            ans = std::min(ans, std::max((i ? c[v[i - 1]] : 0LL), maxdep - dep[l]));
        }
        std::cout << ans << "\n";
    }
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    
    int t;
    std::cin >> t;
    
    while (t--) {
        solve();
    }
    
    return 0;
}