#include <bits/stdc++.h>

template <class T>
inline int qlog(T a) {
	double x = a;
	return ((*(long long*) & x) >> 52 & 2047) - 1023;
}

#define fopen LilyWhite
void fopen(const char *s) {
    static char filename[32];
    sprintf(filename, "%s.in", s);
    freopen(filename, "r", stdin);
    sprintf(filename, "%s.out", s);
    freopen(filename, "w", stdout);
}

typedef unsigned int u32;
typedef long long ll;
typedef unsigned long long u64;

#define Please return
#define AC 0
#define cin Mizuhashi
#define cout Parsee
#define endl '\n'

class Reader{
	private:
	    static const int BUF_SIZE = 1 << 22;
	    char BUF_R[BUF_SIZE], *csy1, *csy2;
	    #ifndef _LOCAL_RUNNING
		    #define GC (csy1 == csy2 && (csy2 = (csy1 = BUF_R) + fread(BUF_R, 1, BUF_SIZE, stdin), csy1 == csy2) ? EOF : *csy1 ++)
		#else
		    char cur;
		    #define GC (cur = getchar())
		#endif
	    #define IL inline
		
    public:
        IL bool eof() {
            #ifndef _LOCAL_RUNNING
                return csy1 == csy2 && (csy2 = (csy1 = BUF_R) + fread(BUF_R, 1, BUF_SIZE, stdin), csy1 == csy2);
            #else
                return cur == EOF;
            #endif
        }
        template <class Ty>
        IL Reader& operator >> (Ty &t) {
            int u = 0;
            char c = GC;
	    	for (t = 0; c < 48 || c > 57; c = GC)
                if (c == EOF) break;
                else if (c == '-') u = 1;
	    	for ( ; c > 47 && c < 58; c = GC) t = t * 10 + (c ^ 48);
	    	t = u ? -t : t; return *this;
        }
    	IL Reader& operator >> (double &t) {
            int tmp, u = 0; char c = GC;
	    	for (tmp = 0; c < 48 || c > 57; c = GC)
                if (c == EOF) break;
                else if (c == '-') u = 1;
	    	for ( ; c > 47 && c < 58; c = GC) tmp = tmp * 10 + (c ^ 48);
	    	t = (tmp = u ? -tmp : tmp);
    	    if (c == '.') {
    	        double x = 1;
    	        for (c = GC; c > 47 && c < 58; c = GC) t += (x /= 10) * (c ^ 48);
    	    }
    	    return *this;
    	}
    	IL Reader& operator >> (char *s) {
			char c = GC;
			for (*s = 0; c < 33; c = GC) if (c == EOF) return *this;
			for ( ; c > 32; c = GC) *s ++ = c;
			*s = 0; return *this;
		}
        IL Reader& operator >> (char &c) {
			for (c = GC; c < 33; c = GC) if (c == EOF) return *this;
            return *this;
        }
}cin;
class Writer{
	private:
	    static const int BUF_SIZE = 1 << 22;
	    char BUF_W[BUF_SIZE], *csy;
	    #define IL inline
		inline void WC(const char c) {
			if (csy - BUF_W == BUF_SIZE) fwrite(BUF_W, 1, BUF_SIZE, stdout), csy = BUF_W;
			*csy ++ = c;
		}
	
	public:
		Writer() : csy(BUF_W) {}
		~ Writer() {fwrite(BUF_W, 1, csy - BUF_W, stdout);}
		IL void flush() {fwrite(BUF_W, 1, csy - BUF_W, stdout); csy = BUF_W;}
		template <class Ty>
		IL Writer& operator << (Ty x) {
		    static int sta[32], top;
			if (x < 0) {
				WC('-');
                do sta[top ++] = - (x % 10); while (x /= 10);
			}else do sta[top ++] = x % 10; while (x /= 10);
			while (top) WC(sta[-- top] ^ 48);
			return *this;
		}
		IL Writer& operator << (const char &c) {WC(c); return *this;}
		IL Writer& operator << (const char *s) {while (*s) WC(*s ++); return *this;}
}cout;

using namespace std;

const int MAX_N = 100000 + 5;

typedef pair <int, int> pii;

int N, M, Q, node[MAX_N];
struct Edge{
    int y, prev, w;
}e[MAX_N << 1];
int elast[MAX_N], ecnt;
char color[MAX_N];
int mark[MAX_N], dep0[MAX_N];
int sz[MAX_N], bs[MAX_N], fa[MAX_N], dep[MAX_N], tp[MAX_N], dfsn[MAX_N], Tm;
ll sum[MAX_N], val0[MAX_N];

inline bool cmp(int i, int j) {
    return dfsn[i] < dfsn[j];
}

void Build(int x, int y, int z) {
    ecnt ++;
    e[ecnt].y = y;
    e[ecnt].prev = elast[x];
    e[ecnt].w = z;
    elast[x] = ecnt;
}

void dfs0(int u, int fath, ll lastR = 0, int depR = 0) {
    sz[u] = 1;
    bs[u] = 0;
    fa[u] = fath;
    dep[u] = dep[fath] + 1;
    if (color[u]) {
        val0[u] = 0;
        depR = dep[u];
        lastR = sum[u];
    }else {
        val0[u] = sum[u] - lastR;
    }
    dep0[u] = depR;
    for (int i = elast[u]; i; i = e[i].prev) {
        int v = e[i].y;
        if (v != fath) {
            sum[v] = sum[u] + e[i].w;
            dfs0(v, u, lastR, depR);
            sz[u] += sz[v];
            if (sz[bs[u]] < sz[v]) bs[u] = v;
        }
    }
}

void dfs1(int u, int gr) {
    tp[u] = gr;
    dfsn[u] = ++ Tm;
    if (bs[u]) dfs1(bs[u], gr);
    for (int i = elast[u]; i; i = e[i].prev) {
        int v = e[i].y;
        if (v != bs[u] && v != fa[u]) dfs1(v, v);
    }
}

int Lca(int u, int v) {
    while (tp[u] != tp[v]) {
        if (dep[tp[u]] < dep[tp[v]]) v = fa[tp[v]];
        else u = fa[tp[u]];
    }
    return dep[u] < dep[v] ? u : v;
}

ll premax[MAX_N], sufmax[MAX_N], f[MAX_N][2], mindep[MAX_N], val1[MAX_N], res;
vector <int> edge[MAX_N];

pii dfs2(int u) {
    int l = N, r = 0;
    if (mark[u]) {
        l = mark[u]; r = mark[u];
        mindep[u] = dep0[u];
        val1[u] = val0[u];
        if (color[u]) f[u][0] = 0;
        else f[u][0] = sum[u];
        f[u][1] = 0;
    }else {
        f[u][0] = 0;
        f[u][1] = 0;
        mindep[u] = N;
        val1[u] = 0;
    }
    for (auto v : edge[u]) {
        pii tmp = dfs2(v);
        l = min(l, tmp.first);
        r = max(r, tmp.second);
        mindep[u] = min(mindep[u], mindep[v]);
        f[u][1] = max(f[u][1], f[v][1]);
        val1[u] = max(val1[u], val1[v]);
        if (mindep[v] < dep[u]) f[u][0] = max(f[u][0], f[v][0]);
        else {
            f[u][1] = max(f[u][1], val1[v]);
        }
    }
    // fprintf(stderr, "u = %d, l = %d, r = %d, pre = %lld, suf = %lld, f = (%lld, %lld), sum = %lld, val1 = %lld, mindep = %d, res = %lld\n",
    //         u, l, r, premax[l - 1], sufmax[r + 1], f[u][0], f[u][1], sum[u], val1[u], mindep[u], max(max(premax[l - 1], sufmax[r + 1]), max(f[u][0] - sum[u], f[u][1])));
    res = min(res, max(max(premax[l - 1], sufmax[r + 1]), max(f[u][0] - sum[u], f[u][1])));
    return {l, r};
}

ll VTsolve(int m) {
    int tot = 0;
    static int a[MAX_N << 1];
    for (int i = 1; i < m; i ++) {
        a[++ tot] = node[i];
        a[++ tot] = Lca(node[i], node[i + 1]);
    }
    a[++ tot] = node[m];
    sort(a + 1, a + tot + 1, cmp);
    tot = unique(a + 1, a + tot + 1) - a - 1;
    for (int i = 1; i <= tot; i ++) edge[a[i]].clear();
    for (int i = 1; i < tot; i ++) {
        int lc = Lca(a[i], a[i + 1]);
        edge[lc].push_back(a[i + 1]);
    }
    res = 1e18;
    dfs2(a[1]);
    return res;
}

void solve() {
    cin >> N >> M >> Q;
    ecnt = 0; Tm = 0;
    memset(elast, 0, sizeof(int) * (N + 1));
    memset(color, 0, N + 1);
    for (int i = 1; i <= M; i ++) {
        int x;
        cin >> x;
        color[x] = 1;
    }
    for (int i = 1; i < N; i ++) {
        int x, y, z;
        cin >> x >> y >> z;
        Build(x, y, z);
        Build(y, x, z);
    }
    dfs0(1, 0); dfs1(1, 1);
    // for (int i = 1; i <= N; i ++) fprintf(stderr, "i = %d, val0 = %lld\n", i, val0[i]);
    while (Q --) {
        int k;
        cin >> k;
        for (int i = 1; i <= k; i ++) cin >> node[i];
        sort(node + 1, node + k + 1, cmp);
        for (int i = 1; i <= k; i ++) {
            mark[node[i]] = i;
            premax[i] = max(premax[i - 1], val0[node[i]]);
        }
        sufmax[k + 1] = 0;
        for (int i = k; i > 0; i --) sufmax[i] = max(sufmax[i + 1], val0[node[i]]);
        cout << VTsolve(k) << endl;
        for (int i = 1; i <= k; i ++) mark[node[i]] = 0;
    }
}

int main() {
    int T;
    cin >> T;
    while (T --) solve();
    return 0;
}