#include <bits/stdc++.h>
/*愉快抄抄aqz*/
#define int long long
using namespace std;
const int MN=1e6+116;
struct Side{
	int u, v, w;
	bool operator <(const Side &o)const{
		return w<o.w;
	}
}side[MN];
int n, k, tot, ans, t[MN];
int lc[MN], rc[MN], val[MN];
int sum1[MN], sum0[MN], val1[MN], val0[MN];
int father[MN], to[MN];
bool vis[MN];
int find(int x){
	if(father[x]!=x) father[x]=find(father[x]);
	return father[x];
}
void dfs1(int u){
	if(!lc[u]&&!rc[u]){
		if(t[u]==0) sum0[u]++;
		else sum1[u]++;
		return;
	}else{
		dfs1(lc[u]); dfs1(rc[u]);
		father[lc[u]]=father[rc[u]]=u;
		sum1[u]=sum1[lc[u]]+sum1[rc[u]];
		sum0[u]=sum0[lc[u]]+sum0[rc[u]];
		vis[u]=(vis[lc[u]]|vis[rc[u]]);
	}
}
void dfs2(int u, int top){
	val0[u]=val0[u]+sum1[u]*val[u]-sum1[u]*val[father[u]];
	val1[u]=val1[u]+sum0[u]*val[u]-sum0[u]*val[father[u]];
	top=(vis[u]?u:top);
	if(!lc[u]&&!rc[u]){
		to[u]=top;
		return;
	}else{
		val0[lc[u]]+=val0[u]; val0[rc[u]]+=val0[u];
		val1[lc[u]]+=val1[u]; val1[rc[u]]+=val1[u];
		dfs2(lc[u],top); dfs2(rc[u],top); 
	}
}
int ask1(int u){
	if(t[u]!=0) return val1[to[u]];
	else return val1[to[u]]-val[to[u]];
}
int ask0(int u){
	if(t[u]!=1) return val0[to[u]];
	else return val0[to[u]]-val[to[u]];
}
void Read(){
	cin>>n>>k; tot=n; for(int i=1; i<=n; ++i) father[i]=i; 
	for(int i=1; i<=n+n; ++i){
		vis[i]=sum1[i]=sum0[i]=val0[i]=val1[i]=0;
		to[i]=val[i]=lc[i]=rc[i]=0;
	}
	for(int i=1; i<=n; ++i) cin>>t[i];
	for(int i=1; i<n; ++i){
		cin>>side[i].u>>side[i].v>>side[i].w;
	}
	sort(side+1,side+n);
	for(int i=1; i<n; ++i){
		++tot; val[tot]=side[i].w; father[tot]=tot;
		int u=find(side[i].u), v=find(side[i].v);
		lc[tot]=u, rc[tot]=v;
		father[u]=father[v]=tot;
	}
	for(int i=1,x; i<=k; ++i){
		cin>>x; vis[x]=true;
	}	
	dfs1(tot); father[tot]=0; dfs2(tot,0);
	int ans=0;
	for(int i=1; i<=n; ++i) if(t[i]==0) ans+=ask0(i);
	cout<<ans<<'\n';
	for(int i=1; i<=n; ++i){
		if(t[i]==0){
			cout<<ans-ask0(i)+ask1(i)<<'\n';
		}else{
			cout<<ans-ask1(i)+ask0(i)<<'\n';
		}
	}
}
signed main(){
	ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	int T; cin>>T; while(T--){
		Read();
	}
	return 0;
}