#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll>pi;
#define int ll
#define X first
#define Y second
#define fer(i,a,n) for(int i=a;i<=n;i++)
#define ref(i,n,a) for(int i=n;i>=a;i--)
#define endl '\n'
#define mem(a,x) memset(a,x,sizeof a)
#define ac IO;int t;cin>>t;while(t--)solve()
#define AC signed main(){IO;solve();}
#define NO {cout<<"No"<<endl;return;}
#define YES {cout<<"Yes"<<endl;return;}
#define re(a) {cout<<a<<endl;return;}
#define all(v) v.begin(),v.end()
//ofstream fout("out.txt", ios::out);
//ifstream fin("in.txt", ios::in);
//#define cout fout
//#define cin fin
//--------------------瑞神神中神--------------------
//--------------------刘魔魔中魔--------------------

const int N=5e5+10;
struct GCD
{
    int f,g;
    int calc(){return gcd(f,g);}
    GCD(int _f=0,int _g=0):f(_f),g(_g){}
    void add(int w)
    {
        f+=w;
    }
    GCD operator+(const GCD&a)const
    {
        if(f==0)return a;
        if(a.f==0)return *this;
        return{f,gcd(g,gcd(abs(a.f-f),a.g))};
    }
}g[N];
int st[N],dis[N],siz[N],ndis,son[N];
int n,k;
vector<pi>e[N];
int ans=1e18;
vector<GCD>vec,pre[N];
GCD ngcd;

void dfs1(int u,int fa)
{
    siz[u]=st[u];
    for(auto[v,w]:e[u])
    {
        if(v==fa)continue;
        son[u]++;
        dfs1(v,u);
        siz[u]+=siz[v];dis[u]+=dis[v];
        dis[u]+=siz[v]*w;
        GCD tmp=g[v];
        if(siz[v])tmp.add(w);
        g[u]=g[u]+tmp;
        if(st[v])g[u]=g[u]+GCD(w,0);
        pre[u].push_back(g[u]);
    }
}

void dfs2(int u,int fa)
{
    ans=min(ans,ndis/(ngcd+g[u]).calc());
    GCD suf={0,0};
    int i=son[u]-1;
    vec.push_back(ngcd);
    for(auto it=e[u].rbegin();it!=e[u].rend();it++)
    {
        auto[v,w]=*it;
        if(v==fa)continue;
        ndis=ndis+(k-siz[v])*w-siz[v]*w;
        ngcd=vec.back();
        ngcd=ngcd+suf;
        if(i>0)ngcd=ngcd+pre[u][i-1];
        if(k-siz[v])ngcd.add(w);
        if(st[u])ngcd=ngcd+GCD(w,0);
        i--;
        suf=suf+g[v];
        dfs2(v,u);
    }
    vec.pop_back();
}

void solve()
{
    cin>>n>>k;
    fer(i,1,k)
    {
        int c;
        cin>>c;
        st[c]=1;
    }
    for(int i=1;i<n;i++)
    {
        int a,b,c;
        cin>>a>>b>>c;
        e[a].emplace_back(b,c);
        e[b].emplace_back(a,c);
    }
    if(k==1)
    {
        cout<<0<<endl;
        return;
    }
    dfs1(1,0);
    ndis=dis[1];ngcd;
    dfs2(1,0);
    cout<<ans*2<<endl;
}

AC