#include <bits/extc++.h>
#include "factories.h"
#define all(v) v.begin(), v.end()
#define zip(v) sort(all(v)), v.erase(unique(all(v)), v.end())
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pint;
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
int n, q;
int sz[500050], use[500050], cent_papa[500050], dep[500050];
vector<pint> adj[500050];
ll m[500050], lv_dist[500050][23];
int get_size(int u, int p=0) {
sz[u]=1;
for(auto& [v, w]:adj[u]) {
if(use[v] || p==v) continue;
sz[u]+=get_size(v,u);
}
return sz[u];
}
int get_cent(int u, int p, int cnt) {
for(auto& [v, w]:adj[u]) {
if(use[v] || v==p) continue;
if(sz[v]>cnt/2) return get_cent(v,u,cnt);
}
return u;
}
void go(int u, int p, int lv) {
for(auto& [v,w]:adj[u]) {
if(use[v] || v==p) continue;
lv_dist[v][lv]=lv_dist[u][lv]+w;
go(v,u,lv);
}
}
void dnc(int u, int p=0, int lv=0) {//p는 이전 cent
int cent=get_cent(u,p,get_size(u,p));
cent_papa[cent]=p;
use[cent]=1;
dep[cent]=lv;
go(cent, 0, lv);
for(auto& [v, w]:adj[cent]) if(!use[v]) dnc(v,cent,lv+1);
}
void update(int u) {
int now=u;
do {
m[now]=min(m[now],lv_dist[u][dep[now]]);
now=cent_papa[now];
} while(now);
}
void downdate(int u) {
int now=u;
do {
m[now]=1e18;
now=cent_papa[now];
} while(now);
}
ll query(int u) {
int now=u;
ll ret=1e18;
do {
ret=min(ret, m[now] + lv_dist[u][dep[now]]);
now=cent_papa[now];
} while(now);
return (ret<1e18) ? ret : -1;
}
void Init(int N, int A[], int B[], int D[]) {
n=N;
for(int i=0;i<n-1;i++) {
adj[A[i]+1].emplace_back(B[i]+1,D[i]);
adj[B[i]+1].emplace_back(A[i]+1,D[i]);
}
dnc(1);
fill(m+1,m+n+1,1e18);
}
long long Query(int S, int X[], int T, int Y[]) {
ll ret=1e18;
for(int i=0;i<S;i++) update(X[i]+1);
for(int i=0;i<T;i++) ret=min(ret,query(Y[i]+1));
for(int i=0;i<S;i++) downdate(X[i]+1);
return ret;
}
