// Title:  旅行者
// Source: GXOI/GZOI2019
// Author: Jerrywang
#include <bits/stdc++.h>
#define ll long long
#define rep(i, s, t) for(int i=s; i<=t; ++i)
#define debug(x) cerr<<#x<<":"<<x<<endl;
const int N=100010; ll inf=0x3f3f3f3f3f3f3f3f;
using namespace std;
mt19937 rnd(time(0));
char buf[1<<23], *p1=buf, *p2=buf;
#define gc() (p1==p2 && (p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?EOF:*p1++)
inline int read()
{
    int x=0, f=1; char c=gc();
    while(c<'0' || c>'9') c=='-' && (f=-1), c=gc();
    while('0'<=c && c<='9') x=(x<<3)+(x<<1)+c-'0', c=gc();
    return x*f;
}

int T, n, m, k, a[N], col[N]; vector<pair<int, int>> g[N];
ll d[N]; bool vis[N];
priority_queue<pair<ll, int>> q;
ll dij()
{
    rep(i, 1, n) d[i]=inf, vis[i]=0;
    rep(i, 1, n) if(col[i]==1)
        d[i]=0, q.push({0, i});
    while(q.size())
    {
        int u=q.top().second; q.pop();
        if(vis[u]) continue; vis[u]=1;
        for(auto [v,w]:g[u]) if(d[u]+w<d[v])
            d[v]=d[u]+w, q.push({-d[v], v});
    }
    ll res=inf;
    rep(i, 1, n) if(col[i]==2) res=min(res, d[i]);
    return res;
}
void solve()
{
    n=read(), m=read(), k=read();
    rep(i, 1, n) g[i].clear();
    rep(i, 1, m)
    {
        int u=read(), v=read(), w=read();
        g[u].push_back({v, w});
    }
    rep(i, 1, k) a[i]=read();
    ll res=inf;
    rep(tt, 1, 40)
    {
        rep(i, 1, k) col[a[i]]=(rnd()&1)+1;
        res=min(res, dij());
    }
    printf("%lld\n", res);
}

int main()
{
#ifdef Jerrywang
    freopen("E:/OI/in.txt", "r", stdin); ios::sync_with_stdio(0);
#endif
    T=read(); while(T--) solve();
    return 0;
}