#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define MAXN 1000005
int n, m, q, k;
ll dp[MAXN], dep[MAXN];
int id[MAXN], tot, lg[MAXN], f[MAXN][20], dep1[MAXN];
vector<pair<int, int>> e[MAXN];
bool vis[MAXN], red[MAXN];
void push(int x, int y, int w) {
	e[x].push_back({y, w});
	e[y].push_back({x, w});
}
void dfs(int x, int fa, ll dis) {
	f[x][0] = fa;
	id[x] = ++tot;
	if(red[x]) dis = dep[x];
	dp[x] = dep[x] - dis;
	dep1[x] = dep1[fa] + 1;
	for(int i=1;i<=lg[dep1[x]];i++) f[x][i] = f[f[x][i-1]][i-1];
	for(auto [v, w] : e[x]) {
		if(v == fa) continue;
		dep[v] = dep[x] + w;
		dfs(v, x, dis);
	}
}
int lca(int x, int y) {
	if(dep1[x] < dep1[y]) swap(x, y);
	while(dep1[x] != dep1[y]) x = f[x][lg[dep1[x]-dep1[y]]];
	if(x == y) return x;
	for(int i=lg[dep1[x]];i>=0;i--) if(f[x][i] != f[y][i])
		x = f[x][i], y = f[y][i];
	return f[x][0];
}

namespace vt{
	vector<pair<int, ll>> e[MAXN];
	void push(int x, int y) {e[x].push_back({y, dep[y] - dep[x]});}
	ll res[MAXN];
	ll dfs(int x, int fa, ll mid) {
		ll ret = 0;
		res[x] = vis[x] && dp[x] > mid ? dep[x] - mid : 0;
		for(auto [v, w] : e[x]) {
			ret += dfs(v, x, mid);
			res[x] = max(res[x], res[v]);
		}
		// printf("x = %d, res = %lld, ret = %lld\n", x, res[x], ret);
		if(!red[x] && res[x] > dep[fa]) ret++, res[x] = 0;
		return ret;
	}
}
int s[MAXN];
bool cmp(int x, int y) {return id[x] < id[y];}
void build(vector<int>& v) {
	sort(v.begin(), v.end(), cmp);
	int top = 0;
	s[top=1] = 1, vt::e[1].clear();
	for(auto x : v) {
		if(x == 1) continue;
		int l = lca(x, s[top]);
		if(l != s[top]) {
			while(id[l] < id[s[top-1]]) vt::push(s[top-1], s[top]), top--;
			if(l != s[top-1]) vt::e[l].clear(), vt::push(l, s[top]), s[top] = l;
			else vt::push(l, s[top--]);
		}
		s[++top] = x, vt::e[x].clear();
	}
	for(int i=1;i<top;i++) vt::push(s[i], s[i+1]);
}

void work() {
	cin>>n>>m>>q;
	for(int i=2;i<=n;i++) lg[i] = lg[i>>1] + 1;
	int x, y, w;
	for(int i=1;i<=m;i++) cin>>x, red[x] = 1;
	for(int i=1;i<n;i++) cin>>x>>y>>w, push(x, y, w);
	dfs(1, 0, 0);
	// for(int i=1;i<=n;i++) printf("dp[%d] = %lld\n", i, dp[i]);
	vector<int> v;
	// puts("------");
	for(int i=1;i<=q;i++) {
		v.clear();
		cin>>k;
		ll l = 0, r = 0, mid, ans;
		for(int j=1;j<=k;j++) cin>>x, v.push_back(x), r = max(r, dp[x]), vis[x] = 1;
		build(v);
		ans = r;
		while(l <= r) {
			mid = (l+r)>>1;
			// printf("mid = %lld, dfs = %lld\n", mid, vt::dfs(1, 0, mid));
			if(vt::dfs(1, 0, mid) <= 1) ans = mid, r = mid-1;
			else l = mid + 1;
		}
		cout << ans << '\n';
		for(auto x : v) vis[x] = 0;
	}
	for(int i=1;i<=n;i++) e[i].clear(), red[i] = 0, vt::e[i].clear();
	tot = 0;
}
int main(){
	// cout << sizeof(f) / 1024 / 1024 << '\n';
ios::sync_with_stdio(false), cin.tie(0);
int t;
	cin>>t;
	while(t--) work();
	return 0;
}