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

int len=0;
char ibuf[(1<<20)+1], *iS, *iT, out[(1<<25)+1];
#define gh() (iS == iT ? iT = (iS = ibuf) + fread(ibuf, 1, (1<<20)+1, stdin), (iS == iT ? EOF : *iS++) : *iS++)

template<typename T>
inline T read()
{
    char ch=gh();
    T x=0;
    char t=0;
    while(ch<'0'||ch>'9')
        t |= ch=='-', ch=gh();
    while(ch>='0'&&ch<='9')
        x = (x<<3) + (x<<1) + (ch^48), ch=gh();
    return t?-x:x;
}

void dfs(int x,int f)
{
    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(x==y) return x;
    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 cost[x]>cost[y];
}

signed main()
{
    T = read<int>();
    while(T--)
    {
        // cin>>n>>m>>q;
        n=read<int>();
        m=read<int>();
        q=read<int>();
        for(int i=1;i<=n;i++)
        {
            red[i]=0;
            ed[i].clear();
        }
        for(int i=1;i<=m;i++)
        {
            int x;
            // cin>>x;
            x=read<int>();
            red[x]=1;
        }
        for(int i=1;i<n;i++)
        {
            int x,y;
            ll z;
            // cin>>x>>y>>z;
            x=read<int>();
            y=read<int>();
            z=read<ll>();
            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--)
        {
            k=read<int>();
            for(int i=1;i<=k;i++)
            {
                key[i]=read<int>();
            }
            sort(key+1,key+1+k,cmp);
            key[k+1]=0;
            ll lasum=0,lca=key[1];
            ll ans=cost[key[1]];
            for(int i=1;i<=k;i++)
            {
                ll nowl=Lca(lca, key[i]);
                ll nowsum=max(lasum+getsum(lca, nowl), getsum(key[i], nowl));
                ans=min(ans, max(nowsum, cost[key[i+1]]));
                lasum=nowsum;
                lca=nowl;
            }
            printf("%lld\n",ans);
        }
    }
    return 0;
}
/*
1
12 2 3
1 3
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
1 2
3 1 3 4
4 1 11 5 12

1
11 1 1
1
1 2 3
2 5 1
2 6 1
1 3 1
3 7 1
3 8 3
1 4 5
4 9 2
4 10 1
7 11 1
2 1 2
*/