/************************************************
* Author        :Running_Time
* Created Time  :2015-8-24 10:48:20
* File Name     :D.cpp************************************************/#include <cstdio>
#include <algorithm>
#include <iostream>
#include <sstream>
#include <cstring>
#include <cmath>
#include <string>
#include <vector>
#include <queue>
#include <deque>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <bitset>
#include <cstdlib>
#include <ctime>
using namespace std;#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
typedef long long ll;
const int N = 1e5 + 10;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
struct UF   {int rt[N], rk[N];void init(void)   {memset (rt, -1, sizeof (rt));memset (rk, 0, sizeof (rk));}int Find(int x)  {return rt[x] == -1 ? x : rt[x] = Find (rt[x]);}void Union(int x, int y) {x = Find (x), y = Find (y);if (x == y) return ;if (rk[x] >= rk[y]) {rt[y] = x;    rk[x] += rk[y];}else  {rt[x] = y;    rk[y] += rk[x];}}bool same(int x, int y)  {return (Find (x) == Find (y));}
}uf;
struct Edge {int u, v, w;bool operator < (const Edge &r) const {return w > r.w;}
};
int n, k;
vector<Edge> G;int main(void)    {int T;  scanf ("%d", &T);while (T--)  {scanf ("%d%d", &n, &k);uf.init ();   G.clear ();ll ans = 0;for (int u, v, w, i=1; i<n; ++i)   {scanf ("%d%d%d", &u, &v, &w);    ans += w;G.push_back ((Edge) {u, v, w});}sort (G.begin (), G.end ());for (int x, i=0; i<k; ++i) {scanf ("%d", &x);    uf.rk[x] = 1;}for (int i=0; i<n-1; ++i)  {int u = G[i].u, v = G[i].v, w = G[i].w;u = uf.Find (u); v = uf.Find (v);if (uf.rk[u] + uf.rk[v] <= 1)    {ans -= w; uf.Union (u, v);}}printf ("%I64d\n", ans);}return 0;
}