#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,int> P;
#define mp(x,y) make_pair(x,y)
const int N = 5e5+10,M = 1e6+10;
int n,m,t,k;
struct made{
    int ver,nx;ll ed;
}e[M<<1];
int hd[N],tot,a[N];
int add(int x,int y,ll z){
    tot++;
    e[tot].ver = y,e[tot].nx = hd[x],e[tot].ed = z,hd[x] = tot;
}
ll d[N];
bool v[N];
void dij(int u){
    memset(d,0x3f,sizeof(d));
    memset(v,0,sizeof(v));
    priority_queue<P,vector<P>,greater<P> >q;
    q.push(mp(0,u));d[u] = 0;
    while(!q.empty()){
        int x = q.top().second;q.pop();
        if(v[x])continue;
        v[x] = 1;
        for(int i = hd[x];i;i = e[i].nx){
            int y = e[i].ver,z = e[i].ed;
            if(d[x] + z < d[y]){
                d[y] = d[x] + z;
                q.push(mp(d[y],y));
            }
        }
    }
}
void first(){
    tot = 0;
    memset(e,0,sizeof(e));
    memset(hd,0,sizeof(hd));
    memset(a,0,sizeof(a));
}
int main(){
    freopen("WAW.in","r",stdin);
    freopen("WAW.out","w",stdout);
    scanf("%d",&t);
    while(t--){
        first();
        scanf("%d%d%d",&n,&m,&k);
        for(int i = 1;i <= m;i++){
            int x,y;ll z;scanf("%d%d%lld",&x,&y,&z);
            add(x,y,z);//单 
        }
        for(int i = 1;i <= k;i++)scanf("%d",&a[i]);
        ll ans = INT_MAX;
        for(int i = 1;i <= k;i++){
            dij(a[i]);
            for(int j = 1;j <= k;j++){
                if(i == j)continue;
                ans = min(ans,d[a[j]]);
            }
        }
        printf("%lld\n",ans);
    }
    
    return 0;
    
}