#include<bits/stdc++.h>
#define L(i, j, k) for(int i = (j); i <= (k); i++)
#define R(i, j, k) for(int i = (j); i >= (k); i--)
#define sz(a) ((int) a.size())
#define vi vector<int>
#define ll long long
#define me(f, x) memset(f, x, sizeof(f))  
#define ull unsigned long long 
using namespace std;
const int N = 4e5 + 7;
template < int N > struct stlca {
	int n;
	int ehd[N], ev[N * 2], enx[N * 2], ew[N * 2], eid;
	void Eadd(int u, int v, int w) {
		enx[++eid] = ehd[u], ev[eid] = v, ew[eid] = w, ehd[u] = eid;
	}
	void add(int u, int v, int w) {
		Eadd(u, v, w);
		Eadd(v, u, w);
	}
	int q[N], s[N], fa[N], lg[N], top;
	ll dep[N];
	int cs[20][N], up[20][N];
	void dfs1(int x) {
		++top, cs[0][q[x] = top] = fa[x];
		up[0][x] = fa[x];
		L(i, 1, 19) {
			up[i][x] = up[i - 1][up[i - 1][x]];
		}
		for(int i = ehd[x]; i; i = enx[i]) if(ev[i] != fa[x]) 
			dep[ev[i]] = dep[x] + ew[i], fa[ev[i]] = x, dfs1(ev[i]);
	}
	inline int cmin(int &x, int &y) {
		return dep[x] < dep[y] ? x : y;
	}
	int lca(int l, int r) {
		if(l == r) return l;
		l = q[l], r = q[r];
		if(l > r) swap(l, r);
		++l;
		int p = lg[r - l + 1];
		return cmin(cs[p][l], cs[p][r - (1 << p) + 1]);
	}
	inline ll dis(int x, int y) { 
		return dep[x] + dep[y] - 2 * dep[lca(x, y)];
	}
	void mk(int xn) {
		n = xn, dfs1(1);
		L(i, 2, top) lg[i] = lg[i >> 1] + 1;
		L(i, 1, 19) L(j, 1, top - (1 << i) + 1) 
			cs[i][j] = cmin(cs[i - 1][j], cs[i - 1][j + (1 << (i - 1))]);
	}
	void clear() {
		L(i, 1, n) ehd[i] = 0, fa[i] = 0;
		top = 0, n = 0, eid = 0;
	}
} ;
stlca < N > st;

struct node {
	int x, y;
	ll dis;
	node() {
		x = y = 0;
		dis = 0;
	}
	void insert(int p) {
		if(!x) return x = p, void();
		if(!y) return y = p, dis = st.dis(x, y), void();
		ll u = st.dis(x, p), v = st.dis(y, p);
		if(max(u, v) <= dis) return ;
		if(u > v) {
			y = p; 
		} else {
			x = p;  
		}
		dis = max(u, v);
	}
};


int n, m, q; 
vector < pair < int, int > > e[N]; 
ll dis[N];
int pos[N], top;
int up[20][N];
inline ll jump(int x, int y) {
	if(!x || !y) return 0;
	int lca = st.lca(x, y);
	ll dx = st.dep[x] - st.dep[lca];
	ll dy = st.dep[y] - st.dep[lca];
	if(dx < dy) swap(dx, dy), swap(x, y);
	ll sum = (dx + dy) / 2;
	
	int z = x;
	R(t, 19, 0) {
		int go = st.up[t][z];
		if(go && st.dep[x] - st.dep[go] <= sum) 
			z = go;
	}
	
	ll ans1 = max(st.dis(x, z), st.dis(y, z));
	z = st.fa[z];
	ll ans2 = z ? max(st.dis(x, z), st.dis(y, z)) : (ll)1e18;
	
//	cout << x << ' ' << y << " : " << z << ' ' << 
//		min(ans1, ans2) << ' ' << st.dis(x, y) << '\n';
	return min(ans1, ans2);
}

void DFS(int x) {
	for(auto E : e[x]) {
		int v = E.first;
		int w = E.second;
		if(v != st.fa[x]) {
			if(dis[v] > dis[x] + w) dis[v] = dis[x] + w;
			DFS(v);
		}
	} 
}
void Main() {
	cin >> n >> m >> q;
	L(i, 1, n) dis[i] = 1e18;
	priority_queue < pair < ll, int > > q;
	L(i, 1, m) {
		int x;
		cin >> x;
		dis[x] = 0;
		q.push({0, x});
	}
	L(i, 1, n - 1) {
		int u, v, w;
		cin >> u >> v >> w;
		e[u].emplace_back(v, w);
		e[v].emplace_back(u, w);
		st.add(u, v, w);
	}
	st.mk(n);
	DFS(1);
	
	while(::q--) {
		cin >> top;
		L(i, 1, top) {
			cin >> pos[i];
		}
		sort(pos + 1, pos + top + 1, [&] (int x, int y) {
			return dis[x] > dis[y];
		});
//		L(i, 1, top) {
//			cout << dis[pos[i]] << ' ';
//		}
//		cout << '\n';
		node qwq;
		ll ans = 1e18;
		ll mxd = 0;
		int rt = 0;
		L(i, 0, top) {
			if(i) {
				if(!rt) rt = pos[i];
				else rt = st.lca(rt, pos[i]); 
				mxd = max(mxd, st.dep[pos[i]]);
			} 
			ll win = rt ? mxd - st.dep[rt] : 0;
			ans = min(ans, max(i == top ? 0LL : dis[pos[i + 1]], win));
		}
		cout << ans << '\n';
	}
	L(i, 1, n) {
		e[i].clear();
	}
	st.clear();
}
int main() {
	ios :: sync_with_stdio (false);
	cin.tie (0); cout.tie (0);
	int t; cin >> t; while(t--) Main();
	return 0;
}