#include<bits/stdc++.h>
using namespace std;
#define FOR(i,s,t) for(int i=(s),_t=(t); i<=_t; ++i)
#define DOR(i,s,t) for(int i=(s),_t=(t); i>=_t; --i)
typedef long long ll;
const int N=1e5+50;
vector<pair<int,int>> E[N];
int col[N];
ll dep[N],pdep[N];
int de[N];
int Fa[N][22];
int Lt[N],Rt[N],tid;
void dfs(int x,int fr,ll d) {
    if(col[x]==1) d=dep[x];
    pdep[x]=d;
    Lt[x]=++tid;
    Fa[x][0]=fr;
    de[x]=de[fr]+1;
    for(auto [y,v]: E[x]) {
        if(y==fr) continue;
        dep[y]=dep[x]+v;
        dfs(y,x,d);
    }
    Rt[x]=tid;
}
int LCA(int x,int y) {
    if(de[x]<de[y]) swap(x,y);
    int d=de[x]-de[y];
    FOR(i,0,20) if((1<<i)&d) x=Fa[x][i];
    if(x==y) return x;
    DOR(i,20,0) if(Fa[x][i]!=Fa[y][i]) {
        x=Fa[x][i],y=Fa[y][i];
    }
    return Fa[x][0];
}
int mark[N];
bool cmp(int x,int y) {
    return dep[x]-pdep[x]>dep[y]-pdep[y];
}
void solve() {
    int n,m,q;
    cin >> n >> m >> q;
    tid=0;
    FOR(i,1,n) E[i].clear();
    FOR(i,1,n) col[i]=0;
    FOR(i,1,m) {
        int x;
        cin >> x;
        col[x]=1;
    }
    FOR(i,2,n) {
        int x,y,w;
        cin >> x >> y >> w;
        E[x].push_back({y,w});
        E[y].push_back({x,w});
    }
    dfs(1,0,0);
    FOR(j,1,20) FOR(i,1,n) Fa[i][j]=Fa[Fa[i][j-1]][j-1];
    while(q--) {
        int K;
        cin >> K;
        vector<int> a;
        while(K--) {
            int x;
            cin >> x;
            a.push_back(x);
        }
        sort(a.begin(),a.end(),cmp);
        ll r=dep[a[0]]-pdep[a[0]];
        int y=0;
        ll mx=0;
        // cerr << LCA(3,8) << endl;
        // cerr << r << endl;
        FOR(i,0,a.size()-1) {
            if(y) y=LCA(y,a[i]);
            else y=a[i];
            mx=max(mx,dep[a[i]]);
            ll t=mx-dep[y];
            if(i+1<a.size()) {
                t=max(t,dep[a[i+1]]-pdep[a[i+1]]);
            }
            // cerr << a[i] << ' ' << t << endl;
            // cerr << y << ' ' << mx << endl;
            r=min(r,t);
        }
        cout << r << '\n';
    }
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int T;
    cin >> T;
    while(T--) solve();
    return 0;
}