#include<iostream>

#include<cstdio>

#include<cmath>

#include<cstdlib>

#include<cstring>

#include<algorithm>

#include<queue>

using namespace std;

#define ll long long

#define N 100010

#define M 500010

char getc(){char c=getchar();while ((c<'A'||c>'Z')&&(c<'a'||c>'z')&&(c<'0'||c>'9')) c=getchar();return c;}

int gcd(int n,int m){return m==0?n:gcd(m,n%m);}

int read()

{

	int x=0,f=1;char c=getchar();

	while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}

	while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();

	return x*f;

}

int n,m,k,p[N],a[N],t;

ll d[N];

bool flag[N];

struct data{int to,nxt,len;

}edge[M];

void addedge(int x,int y,int z){t++;edge[t].to=y,edge[t].nxt=p[x],edge[t].len=z,p[x]=t;}

struct data2

{

	int x;ll d;

	bool operator <(const data2&a) const

	{

		return d>a.d;

	}

};

priority_queue<data2> q;

void dijkstra()

{

	memset(flag,0,sizeof(flag));

	for (;;)

	{

		while (!q.empty()&&flag[q.top().x]) q.pop();

		if (q.empty()) break;

		data2 x=q.top();q.pop();

		flag[x.x]=1;

		for (int i=p[x.x];i;i=edge[i].nxt)

		if (x.d+edge[i].len<d[edge[i].to])

		{

			d[edge[i].to]=x.d+edge[i].len;

			q.push((data2){edge[i].to,d[edge[i].to]});

		}

	}

}

int main()

{

#ifndef ONLINE_JUDGE

	freopen("bzoj5506.in","r",stdin);

	freopen("bzoj5506.out","w",stdout);

	const char LL[]="%I64d\n";

#else

	const char LL[]="%lld\n";

#endif

	int T=read();

	while (T--)

	{

		n=read(),m=read(),k=read();

		memset(p,0,sizeof(p));t=0;

		for (int i=1;i<=m;i++)

		{

			int x=read(),y=read(),z=read();

			addedge(x,y,z);

		}

		for (int i=1;i<=k;i++) a[i]=read();

		ll ans=10000000000000000ll;

		for (int _=18;~_;_--)

		{

			while (!q.empty()) q.pop();

			memset(d,42,sizeof(d));

			for (int i=1;i<=k;i++)

			if (a[i]&(1<<_)) d[a[i]]=0,q.push((data2){a[i],0});

			dijkstra();

			for (int i=1;i<=k;i++)

			if (!(a[i]&(1<<_))) ans=min(ans,d[a[i]]);

			while (!q.empty()) q.pop();

			memset(d,42,sizeof(d));

			for (int i=1;i<=k;i++)

			if (!(a[i]&(1<<_))) d[a[i]]=0,q.push((data2){a[i],0});

			dijkstra();

			for (int i=1;i<=k;i++)

			if (a[i]&(1<<_)) ans=min(ans,d[a[i]]);

		}

		cout<<ans<<endl;

	}

	return 0;

}