#include <bits/stdc++.h>

#define x first
#define y second
#define el '\n'
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
const int N = 1e5 + 10, MAXP = 17;

inline int read() {
    int f = 1, k = 0;
    char c = getchar();
    while (c < '0' || c > '9') {
        if (c == '-') f = -1;
        c = getchar();
    }
    while (c >= '0' && c <= '9') {
        k = k * 10 + c - '0';
        c = getchar();
    }
    return f * k;
}

int n, m, q;
int dep[N], pa[N][MAXP];
ll tored[N], d[N];
bool red[N];
vector<pii> G[N];

void dfs_lca(int u, int fa, int c) {
    pa[u][0] = fa, dep[u] = dep[fa] + 1, d[u] = d[fa] + c;
    if (!red[u]) tored[u] = tored[fa] + c;
    else tored[u] = 0;
    for (int i = 1; i < MAXP; ++i) 
        pa[u][i] = pa[pa[u][i - 1]][i - 1];

    for (auto[v, k] : G[u]) 
        if (v != fa)
            dfs_lca(v, u, k);
}

int lca(int x, int y) {
    if (dep[x] < dep[y]) swap(x, y);
    for (int i = MAXP - 1; i >= 0; --i) if (dep[pa[x][i]] >= dep[y]) x = pa[x][i];
    if (x == y) return x;
    for (int i = MAXP - 1; i >= 0; --i) if (pa[x][i] != pa[y][i]) x = pa[x][i], y = pa[y][i];
    return pa[x][0];
}

bool cmp(int a, int b) {
    return tored[a] < tored[b];
}

void solve() {
    n = read(), m = read(), q = read();
    for (int i = 1; i <= n; ++i) {
        red[i] = 0, G[i].clear();
    }
    while (m--) red[read()] = 1;
    for (int i = 1; i < n; ++i) {
        int u = read(), v = read(), w = read();
        G[u].emplace_back(v, w), G[v].emplace_back(u, w);
    }
    dfs_lca(1, 0, 0);
    while (q--) {
        int k = read();
        vector<int> h(k);
        for (int i = 0; i < k; ++i) h[i] = read();
        sort(h.rbegin(), h.rend(), cmp);
        h.emplace_back(0);
        ll ans = tored[h[0]], mxdis = 0;
        int p = h[0];
        for (int i = 0; i < k; ++i) {
            int x = h[i];
            int l = lca(p, x);
            mxdis += d[p] - d[l];
            mxdis = max(mxdis, d[x] - d[l]);
            p = l;
            // cout << l << ' ' << h[i + 1] << ' ' << mxdis << el;
            ans = min(ans, max(tored[h[i + 1]], mxdis));
        }
        printf("%lld\n", ans);
    }
}

int main() {
    // ios::sync_with_stdio(0); cin.tie(0);
    int tcase = 1;
    cin >> tcase;
    while (tcase--) solve();
}