#include<stdio.h>

#include<string.h>

#include<algorithm>

#define maxn 100010

using namespace std;

#define LL long long

struct node

{

    int x,y;

        LL v;

}edge[maxn];

int pa[maxn],n,m,vis[maxn];

bool cmp(node a,node b)

{

    return a.v>b.v;

}

void init()

{

    int i;

    for(i=;i<=n;i++)

        pa[i]=i;

}

int find (int x)

{

    if(x!=pa[x])

        pa[x]=find(pa[x]);

    return pa[x];

}

void kruskal()

{

    int i,j;

    LL ans=;

    for(i=;i<n-;i++)

    {

        int fx=find(edge[i].x);

        int fy=find(edge[i].y);

        if(vis[fx]&&vis[fy])

        {

            ans+=edge[i].v;

        }

        else if(vis[fx])

            pa[fy]=fx;

        else if(vis[fy])

            pa[fx]=fy;

        else pa[fx]=fy;

    }

    printf("%I64d\n",ans);

}

int main()

{

    int i,j,t;

    scanf("%d",&t);

    while(t--)

    {

        scanf("%d%d",&n,&m);

        init();

        memset(vis,,sizeof(vis));

        for(i=;i<n-;i++)

        {

            scanf("%d%d%lld",&edge[i].x,&edge[i].y,&edge[i].v);

        }

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

        {

            int c;

            scanf("%d",&c);

            vis[c]=;

        }

        sort(edge,edge+n-,cmp);

        kruskal();

    }

}