#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

const int N = 100005, M = N * 2;
int T, n, m, q;

int e, head[N], nxt[M], to[M];
ll d[M];
void adde(int x, int y, ll z)
{
	e++;
	to[e] = y;
	nxt[e] = head[x];
	d[e] = z;
	head[x] = e;
}

int col[N], dd[N];
ll val[N], dep[N];
int f[N][20];
void dfs(int x, int fa)
{
	f[x][0] = fa;
	for (int i = 1; i < 20; i++)
		f[x][i] = f[f[x][i - 1]][i - 1];
	if (col[x]) val[x] = 0;
	for (int i = head[x]; i; i = nxt[i])
	{
		int v = to[i];
		if (v == fa) continue;
		val[v] = val[x] + d[i];
		dep[v] = dep[x] + d[i];
		dd[v] = dd[x] + 1;
		dfs(v, x);
	}
}

int lca(int x, int y)
{
	if (dd[x] < dd[y]) swap(x, y);
	for (int i = 19; i >= 0; i--)
		if (dd[x] - dd[y] >= (1 << i))
			x = f[x][i];
	if (x == y) return x;
	for (int i = 19; i >= 0; i--)
		if (f[x][i] != f[y][i])
		{
			x = f[x][i];
			y = f[y][i];
		}
	return f[x][0];
}

int tt[N];

int main()
{
	scanf("%d", &T);
	while (T--)
	{
		scanf("%d%d%d", &n, &m, &q);
		for (int i = 1; i <= n; i++) col[i] = 0;
		int x, y;
		ll z;
		for (int i = 1; i <= m; i++)
		{
			scanf("%d", &x);
			col[x] = 1;
		}
		e = 0;
		for (int i = 1; i <= n; i++)
			head[i] = 0;
		for (int i = 1; i < n; i++)
		{
			scanf("%d%d%lld", &x, &y, &z);
			adde(x, y, z);
			adde(y, x, z);
		}
		dd[1] = 0;
		dep[1] = 0;
		dfs(1, 0);
		while (q--)
		{
			scanf("%d", &x);
			for (int i = 1; i <= x; i++)
				scanf("%d", &tt[i]);
			ll L = 0, R = 1e15;
			while (L != R)
			{
				ll mid = (L + R) >> 1;
				//printf("erfen %lld\n", mid);
				int l = -1;
				for (int i = 1; i <= x; i++)
				{
					int now = tt[i];
					if (val[now] > mid)
					{
						if (l == -1) l = now;
						else l = lca(l, now);
					}
				}
				bool ok = true;
				for (int i = 1; i <= x; i++)
				{
					int now = tt[i];
					if (val[now] > mid && dep[now] - dep[l] > mid)
					{
						//printf("fail %d %d\n", now, l);
						ok = false;
					}
				}
				if (ok) R = mid;
				else L = mid + 1;
			}
			printf("%lld\n", L);
		}
	}
	return 0;
}