#include<bits/stdc++.h>
#define ioclear std::ios::sync_with_stdio(false);std::cin.tie(nullptr);std::cout.tie(nullptr);
#define endl '\n'
#define CLOCK 1e3 * clock() / CLOCKS_PER_SEC

bool mem1;

using pii = std::pair<int, int>;
using i64 = long long;
constexpr i64 inf = 0x3f3f3f3f3f3f3fll;

void solve()
{
	int n, m, q;
	std::cin >> n >> m >> q;
	std::vector<i64> cost(n + 1, inf), dep(n + 1, 0), dep2(n + 1, 0);
	for(int i = 1, x;i <= m;i++)
	{
		std::cin >> x;
		cost[x] = 0;
	}
	std::vector<std::vector<pii>> edge(n + 1);
	auto add = [&](int u, int v, int w)
	{
		edge[u].emplace_back(v, w);
	};
	for(int i = 1;i < n;i++)
	{
		int u, v, w;
		std::cin >> u >> v >> w;
		add(u, v, w);
		add(v, u, w);
	}
	// const int logn = std::__lg(n);
	std::vector<std::vector<int>> ancestor(n + 1, std::vector<int>(30, 0));
	auto dfs = [&](auto&& self, int cur) -> void
	{
		for(int i = 1;(1 << i) <= dep[cur];i++)
			ancestor[cur][i] = ancestor[ancestor[cur][i - 1]][i - 1];
		for(auto [v, w]: edge[cur])
		{
			if(v == ancestor[cur][0])
				continue;
			ancestor[v][0] = cur;
			dep[v] = dep[cur] + 1;
			dep2[v] = dep2[cur] + w;
			cost[v] = std::min(cost[v], cost[cur] + w);
			self(self, v);
		}
	};
	auto lca = [&](int x, int y) -> int
	{
		if(dep[x] < dep[y])
			std::swap(x, y);
		assert(dep[x] >= dep[y]);
		for(int i = 20;i >= 0;i--)
			if(dep[x] - (1 << i) >= dep[y])
				x = ancestor[x][i];
		if(x == y)
			return x;
		for(int i = 20;i >= 0;i--)
			if(ancestor[x][i] != ancestor[y][i])
				x = ancestor[x][i], y = ancestor[y][i];
		return ancestor[x][0];
	};
	dep[1] = 1;
	// ancestor[1][0] = dep[1] = 0;
	dfs(dfs, 1);
	for(int _ = 1;_ <= q;_++)
	{
		int k;
		std::cin >> k;
		std::vector<int> t(k);
		for(auto& x: t)
			std::cin >> x;
		std::sort(t.begin(), t.end(), [&](int x, int y){return cost[x] < cost[y];});
		int l = t.back();
		i64 Ans = cost[l], maxdep = dep2[l];
		// std::cout << Ans << ' ' << maxdep << endl;
		for(int i = k - 1;i >= 0;i--)
		{
			// std::cout << t[i] << endl;
			// std::cout << "beg: " << Ans << ' ' << l << ' ' << maxdep << endl;
			maxdep = std::max(maxdep, dep2[t[i]]);
			l = lca(l, t[i]);
			Ans = std::min(Ans, std::max((i ? cost[t[i - 1]] : 0ll), maxdep - dep2[l]));
			// std::cout << "end: " << Ans << ' ' << l << ' ' << maxdep << endl;
		}
		std::cout << Ans << endl;
	}
}

bool mem2;

int main()
{
    #ifdef ONLINE_JUDGE
    ioclear;
    #endif
    
    int t;
    std::cin >> t;
    while(t--)
		solve();
    
    // std::cerr << "USED " << CLOCK << " ms\n";
	// fprintf(stderr, "%.3lf MB", (&mem1 - &mem2) / 1048576.0);
}