#include <bits/stdc++.h>
using namespace std;
#define M 200010
#define LL long long
int Red[M];
vector<pair<int, int>> G[M];
int dfn[M], dfs_clock;
int ft[20][M];
LL h[M];
pair<int, int> lca1[M]; int tot;
int dep[M];
LL cost[M];
void dfs(int x, int fa) {
    dfn[x] = ++ dfs_clock;
    ft[0][x] = fa;
    dep[x] = dep[fa] + 1;
    for(int i = 1; i <= 17; ++ i) {
        ft[i][x] = ft[i - 1][ft[i - 1][x]];
    }
    for(auto [v, w] : G[x]) {
        if(v == fa) continue;
        h[v] = h[x] + w;
        dfs(v, x);
    }
}
int lca(int x, int y) {
    if(dep[x] < dep[y]) swap(x, y);
    int t = dep[x] - dep[y];
    for(int i = 0; i <= 17; ++ i) {
        if((t >> i) & 1) {
            x = ft[i][x];
        }
    }
    if(x == y) return x;
    for(int i = 17; i >= 0; -- i) {
        if(ft[i][x] != ft[i][y]) {
            x = ft[i][x], y = ft[i][y];
        }
    }
    return ft[0][x];
}
void dfs1(int x, int fa, int p) {
    cost[x] = h[x] - h[p];
    for(auto [v, w] : G[x]) {
        if(v == fa) continue;
        dfs1(v, x, (Red[v] ? v : p));
    }
}
int V[M];
bool check(int k, LL lim) {
    int L = -1, R = -1, mnpos = -1;
    LL mx = 0;
    for(int i = 1; i <= k; ++ i) {
        if(cost[V[i]] > lim) {
            mx = max(mx, h[V[i]]);
            if(L == -1) L = i;
            R = i;
            if(mnpos == -1) mnpos = i;
            else {
                if(cost[V[i]] < cost[V[mnpos]]) {
                    mnpos = i;
                }
            }
        }
    }
    if(L == -1) return 1;
    int LCA;
    if(lca1[mnpos].first == tot) {
        LCA = lca1[mnpos].second;
    }
    else {
        LCA = lca(V[L], V[R]);
        lca1[mnpos] = {tot, LCA};
    }
    if(mx - h[LCA] <= lim) return 1;
    return 0;
}
void solve() {
    ++ tot;
    int k;
    cin >> k;
    for(int i = 1; i <= k; ++ i) {
        cin >> V[i];
    }
    sort(V + 1, V + k + 1, [](int x, int y){
        return dfn[x] < dfn[y];
    });
    LL l = 0, r = 1e15, t = 0;
    while(l <= r) {
        LL mid = l + r >> 1;
        if(check(k, mid)) r = (t = mid) - 1;
        else l = mid + 1; 
    }
    cout << t << "\n";
}
void Do() {
    int n, m, q;
    cin >> n >> m >> q;
    for(int i = 1; i <= n; ++ i) {
        Red[i] = 0;
    }
    for(int i = 1; i <= m; ++ i) {
        int x;
        cin >> x;
        Red[x] = 1;
    }
    for(int i = 1; i <= n; ++ i) {
        G[i].clear();
    }
    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_clock = 0;
    dfs(1, 0);
    dfs1(1, 0, 1);
    while(q --) {
        solve();
    }
}
int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    int T;
    cin >> T;
    while(T --) {
        Do();
    }
}
/*
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

*/