#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
#define ll long long
#define N 500010
using namespace std;
ll read(){
	char cc;
	while(1){cc=getchar();if((cc>='0'&&cc<='9')||cc=='-')break;}
	ll sum=0,flag=1;
	cc=='-'?flag=-1:sum=(cc^48);
	while(1){cc=getchar();if(!(cc>='0'&&cc<='9'))break;sum=(sum<<1)+(sum<<3)+(cc^48);}
	return sum*flag;
}
void write(ll x){
	if(!x)putchar('0');
	if(x<0){x=-x;putchar('-');}
	ll cc[25],cntt=0;
	while(x){cc[++cntt]=x%10;x/=10;}
	for(ll i=cntt;i>=1;i--)putchar(cc[i]+'0');
	putchar('\n');
}
vector <pair<ll,ll> > b[N];
ll T,n,m,q,a[N],d[N],d1[N],f[N][20],d2[N],ans,c[N],k;
ll cmp(ll a,ll b){return d1[a]<d1[b];}
void dfs(ll x,ll faa){
	f[x][0]=faa;
	if(a[x])d1[x]=0;
	for(pair<ll,ll> y:b[x]){
		ll v=y.first,w=y.second;
		if(v==faa)continue;
		d[v]=d[x]+w;
		d1[v]=d1[x]+w;
		d2[v]=d2[x]+1;
		dfs(v,x);
	}
}
ll lca(ll x,ll y){
	if(d2[x]<d2[y])swap(x,y);
	for(ll i=17;i>=0;i--)if(d2[f[x][i]]>=d2[y])x=f[x][i];
	if(x==y)return x;
	for(ll i=17;i>=0;i--)if(f[x][i]!=f[y][i])x=f[x][i],y=f[y][i];
	return f[x][0];
}
int main(){
	T=read();
	while(T--){
		n=read();m=read();q=read();
		for(ll i=1;i<=n;i++)a[i]=0;
		while(m--)a[read()]=1;
		for(ll i=1;i<=n;i++)b[i].clear();
		for(ll i=1;i<n;i++){
			ll u=read(),v=read(),w=read();
			b[u].push_back(make_pair(v,w));
			b[v].push_back(make_pair(u,w));
		}
		dfs(1,0);
		for(ll j=1;j<=17;j++)for(ll i=1;i<=n;i++)f[i][j]=f[f[i][j-1]][j-1];
		while(q--){
			k=read();for(ll i=1;i<=k;i++)c[i]=read();
			if(k==1){putchar('0');putchar('\n');continue;}
			sort(c+1,c+k+1,cmp);
			ll ans=d1[c[k-1]];
			ll lcaa=c[k],maxd=d[c[k]];
			for(ll i=k-1;i>=1;i--){
				lcaa=lca(lcaa,c[i]);
				maxd=max(maxd,d[c[i]]);
				ans=min(ans,max(maxd-d[lcaa],d1[c[i-1]]));
				if(maxd-d[lcaa]>d1[c[i-1]])break;
			}
			write(ans);
		}
	}
	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
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


*/