#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<cmath>
#include<cstdlib>
#include<algorithm>
using namespace std;
int n,k,fa[100010],mark[100010];
struct node
{
    int x,y,z;
}e[100010];
bool cmp(node a,node b)
{
    return a.z>b.z;
}
int find(int x)
{
    if(x!=fa[x])
        fa[x]=find(fa[x]);
    return fa[x];
}
int main()
{
    int tt,x;
    scanf("%d",&tt);
    while(tt--)
    {
        long long ans=0;
        scanf("%d%d",&n,&k);
        memset(mark,0,sizeof(mark));
        for(int i=0;i<n;i++)
            fa[i]=i;
        for(int i=0;i<n-1;i++)
            scanf("%d%d%d",&e[i].x,&e[i].y,&e[i].z),ans+=e[i].z;
        sort(e,e+n-1,cmp);
        while(k--)
        {
            scanf("%d",&x);
            mark[x]=1;
        }
        for(int i=0;i<n-1;i++)
        {
            int fx,fy;
            fx=find(e[i].x);
            fy=find(e[i].y);
            if(mark[fx]+mark[fy]<=1)
            {
                if(fx!=fy)
                {
                    fa[fx]=fy;
                    mark[fy]+=mark[fx];
                }
                ans-=e[i].z;
            }
        }
        printf("%I64d\n",ans);
    }
    return 0;
}