#include <bits/stdc++.h>
#define pb emplace_back
using pii = std::pair<long long,int>;
using i64 = long long;

const int maxn = 1e5 + 5;
const int maxm = 5e5 + 5;
std::vector<std::pair<int,int> > G[maxn];
int n,m,k,a[maxn];
std::priority_queue<pii,std::vector<pii>,std::greater<pii> > q;
bool vis[maxn];
i64 dis[maxn];

void dijkstra(int s) {
	memset(vis , false , sizeof(vis));
	for(int i = 0;i <= n + 1;++ i)
		dis[i] = 1e16;
	q.emplace(dis[s] = 0 , s);
	while(!q.empty()) {
		int u = q.top().second;
		q.pop();
		if(vis[u])continue ;
		vis[u] = true;
		for(auto& [v , w] : G[u]) {
			if(dis[v] > dis[u] + w) {
				q.emplace(dis[v] = dis[u] + w , v);
			}
		}
	}
	return ;
}

void work() {
	scanf("%d %d %d",&n,&m,&k);
	for(int i = 0;i <= n + 1;++ i)
		G[i].clear();
	for(int i = 1;i <= m;++ i) {
		int u,v,t;
		scanf("%d %d %d",&u,&v,&t);
		G[u].pb(v , t);
	}
	for(int i = 1;i <= k;++ i)
		scanf("%d",&a[i]);
	
	i64 ans = 1e16;
	int s = 0,t = n + 1;
	for(int p = 17;~ p;-- p) {
		G[s].clear();
		G[t].clear();
		for(int i = 1;i <= k;++ i)
			if((~ a[i]) >> p & 1)G[s].pb(a[i] , 0);
			else G[t].pb(a[i] , 0);
		dijkstra(s);
		for(int i = 1;i <= k;++ i)
			if(a[i] >> p & 1)ans = std::min(ans , dis[a[i]]);
		dijkstra(t);
		for(int i = 1;i <= k;++ i)
			if((~ a[i]) >> p & 1)ans = std::min(ans , dis[a[i]]);
	}
	
	printf("%lld\n",ans);
	return ;
}

int main() {
	freopen("WAW.in","r",stdin);
	freopen("WAW.out","w",stdout);
	int T;
	scanf("%d",&T);
	while(T --)work();
	return 0;
}