#include<bits/stdc++.h>
using namespace std;

int n,m,q,T;
int col[100005];
vector<pair<int,int>> E[100005];
int st[19][200005],dfn[100005],pos[100005],idfn[100005],dcnt,scnt;
long long dep[100005],ans[100005];
int Q[200005],_2[200005];

class FASTIO{
	public:
		long long read(){
			char c;long long x=0,f=1;
			do{c=getchar();if(c=='-')f=-1;}while(c<'0' || c>'9');
			while(c>='0' && c<='9'){x=(x<<3)+(x<<1)+c-'0';c=getchar();}
			return x*f;
		}
		void write(long long x){
			if(x<0)putchar('-'),x=-x;
			if(x>=10)write(x/10);
			putchar(x%10+'0');
		}
		FASTIO &operator >> (int &x){x=read(); return *this;}
		FASTIO &operator << (int x){write(x);return *this;}
		FASTIO &operator >> (long long &x){x=read(); return *this;}
		FASTIO &operator << (long long x){write(x);return *this;}
		FASTIO &operator >> (char* c){scanf("%s",c);return *this;}
		FASTIO &operator << (char* c){printf("%s",c);return *this;}
		FASTIO &operator >> (char &c){c=getchar();return *this;}
		FASTIO &operator << (char c){putchar(c);return *this;}
}FIO;

void dfs(int x,int f){
	dfn[x]=++dcnt;
	idfn[dcnt]=x;
	st[0][pos[x]=++scnt]=dfn[x];
	for(auto it:E[x]){
		if(it.first==f)continue;
		dep[it.first]=dep[x]+it.second;
		if(col[it.first])ans[it.first]=0;
		else ans[it.first]=it.second+ans[x];
		dfs(it.first,x);
		st[0][++scnt]=dfn[x];
	}
}
void init(){
	for(int i=1;i<=18;++i){
		for(int j=1;j+(1<<(i-1))<=scnt;++j)
			st[i][j]=min(st[i-1][j],st[i-1][j+(1<<(i-1))]);
	}
}

int lca(int x,int y){
	x=pos[x],y=pos[y];if(x>y)swap(x,y);
	int l=_2[y-x+1];
	return idfn[min(st[l][x],st[l][y-(1<<l)+1])];
}

int cmp(int x,int y){
	return ans[x]>ans[y];
}

void solve(){
	FIO>>n>>m>>q;
	for(int i=1;i<=n;++i)col[i]=0,E[i].clear();
	for(int i=1,ui;i<=m;++i)FIO>>ui,col[ui]=1;
	for(int i=1,ui,vi,wi;i<n;++i)FIO>>ui>>vi>>wi,E[ui].push_back({vi,wi}),E[vi].push_back({ui,wi});
	dcnt=scnt=0;dfs(1,0);init();
	while(q--){
		int qi,l;FIO>>qi;
		for(int i=0;i<qi;++i)FIO>>Q[i];
		sort(Q,Q+qi,cmp);
		long long ANS=ans[Q[0]],sum=0;l=Q[0];
		for(int i=0;i<qi;++i){
			l=lca(Q[i],l);
			sum=max(sum,dep[Q[i]]);
			long long ANS1=sum-dep[l];
			long long ANS2=(i+1==qi)?0:ans[Q[i+1]];
			ANS=min(ANS,max(ANS1,ANS2));
		}
		FIO<<ANS<<'\n';
	}
}


int main(){
//	freopen("1.in","r",stdin);
//	freopen("1.out","w",stdout);
	for(int i=2;i<=200000;++i)_2[i]=_2[i>>1]+1;
	scanf("%d",&T);
	while(T--)solve();
}