#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define cmin(a, b) a = min(a, b)
const int inf = 1e18;
const int LOG=20;
int n;
vector<vector<pair<int, int>>> adj, up;
vector<int> depth;
void dfsinit(int u, int p) {
for (auto [v, w]: adj[u]) if (v!=p) {
up[v][0]={u, w};
for (int i=1; i<LOG; i++) {
if (up[v][i-1].fi==-1) break;
up[v][i]=up[up[v][i-1].fi][i-1];
up[v][i].se+=up[v][i-1].se;
}
depth[v]=depth[u]+1;
dfsinit(v, u);
}
}
pair<int, int> lca(int a, int b) {
if (a==b) return {a, 0};
if (depth[a]<depth[b]) swap(a, b);
int ans=0;
int k=depth[a]-depth[b];
for (int i=0; i<LOG; i++) if (k&(1<<i)) ans+=up[a][i].se, a=up[a][i].fi;
if (a==b) return {a, ans};
for (int i=LOG-1; i>=0; i--) if (up[a][i].fi!=up[b][i].fi) {
ans+=up[a][i].se+up[b][i].se;
a=up[a][i].fi, b=up[b][i].fi;
}
return {up[a][0].fi, ans+up[a][0].se+up[b][0].se};
}
int dist(int a, int b) {
return lca(a, b).se;
}
vector<int> sz, centro, par;
void dfs(int u, int p) {
sz[u]=1;
for (auto [v, w]: adj[u]) if (v!=p && !centro[v]) {
dfs(v, u);
sz[u]+=sz[v];
}
}
int centroid(int u, int p, int obj) {
for (auto [v, w]: adj[u]) if (v!=p && !centro[v]) {
if (sz[v]*2>=obj) return centroid(v, u, obj);
}
return u;
}
int decompose(int u, int p) {
if (centro[u]) return u;
dfs(u, u);
int c=centroid(u, u, sz[u]); centro[c]=1;
par[c]=p;
for (auto [v, w]: adj[c]) if (!centro[v]) {
decompose(v, c);
}
return c;
}
vector<int> distres;
void update(int u, int changing=-1) {
if (changing==-1) changing=u;
if (u==-1) return;
cmin(distres[u], dist(u, changing));
update(par[u], changing);
}
void reset(int u, int changing=-1) {
if (changing==-1) changing=u;
if (u==-1) return;
distres[u]=inf;
reset(par[u], changing);
}
int query(int u, int changing=-1) {
if (changing==-1) changing=u;
if (u==-1) return inf;
return min(distres[u]+dist(u, changing), query(par[u], changing));
}
void Init(signed N, signed A[], signed B[], signed D[]) {
n=N;
adj.resize(n);
for (int i=0; i<n-1; i++) {
adj[A[i]].push_back({B[i], D[i]});
adj[B[i]].push_back({A[i], D[i]});
}
up.resize(n, vector<pair<int, int>>(LOG, {-1, 0}));
depth.resize(n), sz.resize(n), centro.resize(n), par.resize(n, -1);
dfsinit(0, 0);
decompose(0, -1);
distres.resize(n, inf);
}
int Query(signed S, signed X[], signed T, signed Y[]) {
int ans=inf;
for (int i=0; i<S; i++) update(X[i]);
for (int i=0; i<T; i++) cmin(ans, query(Y[i]));
for (int i=0; i<S; i++) reset(X[i]);
return ans;
}
