#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int T;
int n,m,q,k;
int dfn[100010],timee;
int key[100010];
int a[100010<<2],tot,root;
bool red[100010],kk[100010];
vector<pair<int, ll> > ed[100010],eed[100010];
int fa[100010][21],deep[100010];
ll sum[100010][21];
ll cost[100010];

void dfs(int x,int f)
{
    dfn[x]=++timee;
    for(int i=1;i<=20;i++)
    {
        fa[x][i]=fa[fa[x][i-1]][i-1];
        sum[x][i]=sum[fa[x][i-1]][i-1]+sum[x][i-1];
    }
    for(auto i:ed[x])
    {
        int v=i.first;
        ll val=i.second;
        if(v==f) continue;
        deep[v]=deep[x]+1;
        fa[v][0]=x;
        sum[v][0]=val;
        dfs(v, x);
    }
}

void dfs1(int x,int f,ll ss)
{
    if(red[x]) ss=0;
    cost[x]=ss;
    for(auto i:ed[x])
    {
        int v=i.first;
        ll val=i.second;
        if(v==f) continue;
        dfs1(v, x, ss+val);
    }
}

int lca(int x,int y)
{
    if(deep[x]<deep[y]) swap(x,y);
    for(int i=20;i>=0;i--)
    {
        int xx=fa[x][i];
        if(deep[xx]>=deep[y])
        {
            x=xx;
        }
    }
    if(x==y) return x;
    for(int i=20;i>=0;i--)
    {
        int xx=fa[x][i];
        int yy=fa[y][i];
        if(xx!=yy)
        {
            x=xx;
            y=yy;
        }
    }
    return fa[x][0];
}

ll getsum(int x,int y)
{
    ll res=0;
    for(int i=20;i>=0;i--)
    {
        int xx=fa[x][i];
        if(deep[xx]>=deep[y])
        {
            res+=sum[x][i];
            x=xx;
        }
    }
    return res;
}

bool cmp(int x,int y)
{
    return dfn[x]<dfn[y];
}

int id;
ll ans;
ll high[100010];
int fff[100010];
bool maxvis[100010];
int sikey[100010];
void DFS(int x)
{
    if(x==id) maxvis[x]=1;
    if(kk[x]) sikey[x]++;
    for(auto i:eed[x])
    {
        int v=i.first;
        ll val=i.second;
        fff[v]=x;
        DFS(v);
        sikey[x]+=sikey[v];
        maxvis[x]|=maxvis[v];
        high[x]=max(high[x], high[v]+val);
    }
}

int lefkey[100010],silef;
void DFS1(int x)
{
    for(auto i:eed[x])
    {
        int v=i.first;
        ll val=i.second;
        if(maxvis[v])
        {
            DFS1(v);
            if(kk[v]) lefkey[++silef]=v;
            break;
        }
    }
    for(auto i:eed[x])
    {
        int v=i.first;
        ll val=i.second;
        if(maxvis[v]) continue;
        DFS1(v);
        if(kk[v]) lefkey[++silef]=v;
    }
}

ll backmaxx[100010];
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout.tie(0);
    cin>>T;
    while(T--)
    {
        cin>>n>>m>>q;
        timee=0;
        for(int i=1;i<=n;i++)
        {
            red[i]=0;
            ed[i].clear();
            dfn[i]=0;
        }
        for(int i=1;i<=m;i++)
        {
            int x;
            cin>>x;
            red[x]=1;
        }
        for(int i=1;i<n;i++)
        {
            int x,y;
            ll z;
            cin>>x>>y>>z;
            ed[x].push_back(make_pair(y, z));
            ed[y].push_back(make_pair(x, z));
        }
        deep[1]=1;
        dfs(1,0);
        dfs1(1, 0, 0);
        while(q--)
        {
            cin>>k;
            // cout<<"cost:\n";
            for(int i=1;i<=k;i++)
            {
                cin>>key[i];
                kk[key[i]]=1;
                // cout<<cost[key[i]]<<" ";
            }
            // puts("");
            tot=0;
            sort(key+1,key+k+1,cmp);
            for(int i=1;i<k;i++)
            {
                int tem=lca(key[i],key[i+1]);
                a[++tot]=key[i];
                a[++tot]=tem;
            }
            a[++tot]=key[k];
            
            sort(a+1,a+1+tot,cmp);
            tot=unique(a+1,a+1+tot)-(a+1);
            // cout<<"vt:\n";
            for(int i=1;i<=tot;i++)
            {
                // cout<<a[i]<<" ";
                eed[a[i]].clear();
                fff[a[i]]=0;
                maxvis[a[i]]=0;
                high[a[i]]=0;
                sikey[a[i]]=0;
            }
            // puts("");
            // puts("");
            root=a[1];
            // cout<<"bt:\n";
            for(int i=1;i<tot;i++)
            {
                int tem=lca(a[i],a[i+1]);
                ll val=getsum(a[i+1], tem);
                // cout<<tem<<" "<<a[i+1]<<endl;
                eed[tem].push_back(make_pair(a[i+1], val));
            }
            id=0;
            ans=0;
            // cout<<"!\n";
            for(int i=1;i<=k;i++)
            {
                // cout<<key[i]<<" "<<cost[key[i]]<<endl;
                if(cost[key[i]]>ans)
                {
                    ans=cost[key[i]];
                    id=key[i];
                }
            }
            // cout<<id<<endl;
            // cout<<ans<<endl;
            silef=0;
            DFS(root);
            DFS1(root);
            backmaxx[silef+1]=0;
            // for(int i=1;i<=silef;i++)
            // {
            //     cout<<lefkey[i]<<" ";
            // }
            // puts("");
            // puts("");
            for(int i=silef;i>=1;i--)
            {
                backmaxx[i]=max(backmaxx[i+1], cost[lefkey[i]]);
            }
            while(id!=0)
            {
                if(!red[id])
                {
                    int nowsi=sikey[id];
                    ll backmax=backmaxx[nowsi+1];
                    // cout<<id<<endl;
                    // cout<<backmax<<" "<<high[id]<<endl;
                    ans=min(ans, max(backmax, high[id]));
                }
                id=fff[id];
            }
            for(int i=1;i<=k;i++) kk[key[i]]=0;
            cout<<ans<<'\n';
        }
    }
    return 0;
}
/*
2
12 2 4
1 9
1 2 1
2 3 4
3 4 3
3 5 2
2 6 2
6 7 1
6 8 2
2 9 5
9 10 2
9 11 3
1 12 10
3 3 7 8
4 4 5 7 8
4 7 8 10 11
3 4 5 12
3 2 3
1 2
1 2 1
1 3 1
1 1
2 1 2
3 1 2 3
*/