#include <bits/stdc++.h>
using namespace std;
#define C const
#define U unsigned
#define SC static
#define CE constexpr
#define TL template
#define TN typename
#define OP operator
#define pb push_back
#define ft first
#define sd second
#define mi (l + (r - l) / 2)
#define TTT TL<TN T>
#define TTI TL<TN It>
#define BE(v) v.begin(), v.end()
#define VD void
#define BL bool
#define CH char
#define I int
#define LL long long
#define II __int128
#define D double
using PII = pair<I, I>;
TTT using V = vector<T>;

#define FORX(v) for(auto& x : v)
#define FOR(i, b, e)  for(auto i = b, _e = (decltype(i))e;i < _e; ++i)
#define FORR(i, b, e) for(auto i = b, _e = (decltype(i))e;i > _e; --i)
#define FORV(v, i) for (I i = 0, _n = v.size(), x = _n ? v[0] : 0;i < _n;x = v[++i])
#define FUNC(T, f, ...) function<T(__VA_ARGS__)> f = [&](__VA_ARGS__)->T

#define DR(T, ...) T __VA_ARGS__; R(__VA_ARGS__);
TTT VD R(T& x) { cin >> x; }
TTT T R() { DR(T, x); return x; }
TL<TN T, TN... A> VD R(T& x, A&... a) { R(x), R(a...); }
CE CH LF = '\n', SP = ' ';
TL<CH s = LF> VD W() { cout << s; }
TL<CH s = LF, TN T> VD W(C T& x) { cout << x << s; }
TL<CH s = LF, TN T, TN... A> VD W(C T& x, C A&... a) { W<SP>(x), W<s>(a...); }

TTT CE T inf() { return numeric_limits<T>::max() / 2; }
TTT VD setmin(T& a, C T& b) { if (b < a)a = b; }
TTT VD setmax(T& a, C T& b) { if (a < b)a = b; }

TTT VD fastpow(T& a, T b, LL i) { for (;i;i >>= 1, b *= b)if (i & 1)a *= b; }
TTT VD fastgss(T& a, C T& b, LL i, U I j = 64)
{
	while (!(i >> --j & 1));
	for (T c = b;j-- && (a += a * c, c *= c, 1);)if (i >> j & 1)a += c, c *= b;
}

#define OPD(T,S,op,...) \
T& OP op##= (C S& _){{__VA_ARGS__} return *this;}\
friend T OP op (C T& a, C S& b) {T c = a; return c op##= b;}
#define OPB(T,op,...) friend BL OP op (C T& a, C T& b) {return __VA_ARGS__;}
#define OST(T) friend ostream& OP << (ostream & os, C T & a) { return os << a.x; }

struct Mod//WARNING : Mod MUST BE assigned in [0,m) unless using cc
{
	SC U I m; SC U LL i;
	SC VD set(U I mod) { m = mod, i = (U LL)(-1) / m + 1; }
	SC U I mul(U I a, U I b)
	{
		U LL x = (U LL)a * b, y = ((U II)x * i >> 64) * m;
		return x - y + (x < y ? m : 0);
	}
	U I x; CE Mod() :x(0) {}
	TTT CE Mod(T x) : x(x) {}
	TTT CE SC Mod cc(T x) { return (x % m + m) % m; }
	OPD(Mod, Mod, +, if ((x += _.x) >= m)x -= m;);
	OPD(Mod, Mod, -, if ((x += m - _.x) >= m)x -= m;);
	OPD(Mod, Mod, *, x = mul(x, _.x););
	OPD(Mod, Mod, / , fastpow(*this, _, m - 2););//m must be a prime
	OPD(Mod, I, ^, fastpow(*this, *this, _ - 1 + (_ > 0 ? 0 : m - 1)););
	OPB(Mod, == , a.x == b.x);
	OPB(Mod, != , a.x != b.x);
	OST(Mod)
};
U I Mod::m; U LL Mod::i;

TL<TN T, VD(*add)(T& c, C T& a, C T& b)> struct VT//VirtualTree
{
	I n, d, rt; V<I> dp, rk; V<V<I>> f; V<V<T>> h;
	VT(C V<V<I>>& e, C V<V<T>>& g, I rt = 1) :n(e.size()), d(ilogb(n)), rt(rt),
		dp(n), rk(n), f(d + 1, V<I>(n)), h(d + 1, V<T>(n))
	{
		I num = 0;
		FUNC(VD, dfs, I p)
		{
			rk[p] = num++;
			FORV(e[p], i)if (x != f[0][p])
				dp[x] = dp[f[0][x] = p] + 1, h[0][x] = g[p][i], dfs(x);
		};
		dp[rt] = 1; dfs(rt);
		FOR(k, 0, d)FOR(i, 1, n)
		{
			f[k + 1][i] = f[k][f[k][i]];
			add(h[k + 1][i], h[k][i], h[k][f[k][i]]);
		}
	}
	I lca(I x, I y)
	{
		if (dp[x] < dp[y])swap(x, y);
		FORR(k, d, -1)if (dp[f[k][x]] >= dp[y])x = f[k][x];
		if (x == y)return x;
		FORR(k, d, -1)if (f[k][x] != f[k][y])x = f[k][x], y = f[k][y];
		return f[0][x];
	}
	T sum(I p, I x)
	{
		T res = h[0][x], tmp; x = f[0][x];
		FORR(k, d, -1)if (dp[f[k][x]] >= dp[p])
			add(res, tmp = res, h[k][x]), x = f[k][x];
		return res;
	}
	VD OP()(V<I> a, V<I>& is, V<V<I>>& e, V<V<T>>& g)
	{
		FORX(a)is[x] = -1;
		sort(BE(a), [&](I x, I y) {return rk[x] < rk[y];});
		FOR(i, 0, a.size())a.pb(i ? lca(a[i - 1], a[i]) : rt);
		sort(BE(a), [&](I x, I y) {return rk[x] < rk[y];});
		a.resize(unique(BE(a)) - a.begin());
		FORX(a)is[x] = is[x] == -1;
		e[rt].clear(), g[rt].clear();
		FOR(i, 1, a.size())
		{
			I u = lca(a[i - 1], a[i]), v = a[i];
			T w = sum(u, v);
			e[u].pb(v), e[v].assign({ u });
			g[u].pb(w), g[v].assign({ w });
		}
	}
};
VD add(LL& c, C LL& a, C LL& b) { c = a + b; }
VD test()
{
	DR(I, n, m, q); ++n;
	V<I> isr(n), is(n);
	V<V<I>> te(n), e(n); V<V<LL>> tg(n), g(n);
	while (m--)isr[R<I>()] = 1;
	FOR(i, 2, n)
	{
		DR(I, u, v, w);
		te[u].pb(v), tg[u].pb(w);
		te[v].pb(u), tg[v].pb(w);
	}
	VT<LL, add> vt(te, tg);
	if(n>1000)return;
	FUNC(LL, dfs, I p, I fa, LL w, LL lim, I & cnt)
	{
		LL res = 0;
		FORV(e[p], i)
		{
			if (x == fa)continue;
			setmax(res, dfs(x, p, g[p][i], lim, cnt));
		}
		if (!isr[p] && res + w > lim) { ++cnt;return 0; }
		return isr[p] ? 0 : res + w;
	};
	FUNC(BL, check, LL lim)
	{
		I cnt = 0;
		dfs(1, 0, 0, lim, cnt);
		return cnt <= 1;
	};
	while (q--)
	{
		V<I> a;DR(I, k);while (k--)a.pb(R<I>());
		vt(a, is, e, g);
		LL l = -1, r = inf<LL>();
		while (l + 1 < r)(!check(mi) ? l : r) = mi;
		W(r);
	}
}

I main()
{
	ios::sync_with_stdio(0);
	cin.tie(0), cout.tie(0);
	if (fopen("test.in", "r"))
	{
		freopen("test.in", "r", stdin);
		freopen("test.out", "w", stdout);
	}
	I t = 1;
	R(t);
	while (t--)test();
	return 0;
}