#include <bits/stdc++.h>
using namespace std;
const int M=500010;
typedef long long ll;
ll t,n,m,k,a[M],b[M],c[M],mk[M],tot,cnt,maxx,cnt1,cnt2,dis[M],res=1e9+10;
ll head[M];
inline ll read(){
    ll x = 0,f = 1; char c = getchar();
    while (c != EOF && !isdigit(c)) {if (c == '-') f = -1;c = getchar();}
    while (isdigit(c)) {x = x * 10 + c - '0';c = getchar();}
    return x * f;
}
struct node {
	ll v,w,nxt;
}e[M];
void add (ll u,ll v,ll w) {
	e[++tot].v=v;
	e[tot].w=w;
	e[tot].nxt=head[u];
	head[u]=tot;
}
struct edge {
	ll t,dis;
    bool operator <(const edge &o) const{
    	return o.dis<dis;
	}
};
void dij (int s) {
	priority_queue<edge>q;
	dis[s]=0;
	q.push((edge){s,0});
	while(!q.empty()) {
		ll t=q.top().dis;
		ll u=q.top().t;
		q.pop();
		if (mk[u]) continue;
		mk[u]=1;
		//cout << u <<' '<< t <<endl;
		for (int i=head[u];i;i=e[i].nxt) {
			long long v=e[i].v,w=e[i].w;
			//cout << w <<endl;
			if (dis[v]>dis[u]+w) {
				dis[v]=dis[u]+w;
				//cout << v <<' '<< u <<' '<< dis[v] <<endl;
				q.push((edge){v,dis[v]});
			}
		}
	}
}
int main () {
	freopen("WAW.in","r",stdin);
	freopen("WAW.out","w",stdout);
	//cout << (10&(1<<3)) <<endl;
	t=read();
	//memset(dis,0x3f,sizeof(dis));
	while (t--) {
		cnt=0,res=1e9+10;
		n=read(),m=read(),k=read();
		tot=0;
		for (int i=1;i<=n;i++) head[i]=0;
		for (int i=1;i<=m;i++) {
			long long a,b,c;
			a=read(),b=read(),c=read();
			add(a,b,c);
		}
		for (int i=1;i<=k;i++) {
			a[i]=read();
		}
		//for (long long j=1;j<=cnt1;j++) cout << b[j] <<' ';
		//cout <<endl;
		//for (long long j=1;j<=cnt2;j++) cout << c[j] <<' ';
		//cout <<endl;
		//cout << cnt1 <<' '<< cnt2 <<endl;
		//if (cnt1==0||cnt2==0) continue;
		for (int i=1;i<=k;i++) {
			for (int j=1;j<=n;j++) {
				dis[j]=1e9+10;
				mk[j]=0;
			}
			dij(a[i]);
			for (int j=1;j<=k;j++) {
				if (i==j) continue;
				//cout << dis[c[k]] <<' ';
				res=min(res,dis[a[j]]);
			}
			//cout <<endl;
		}
		printf("%d\n",res);
	}
	return 0;
}