#include "factories.h"
#include <bits/stdc++.h>
#define int long long
#define fi first
#define se second
#define pb push_back
#define mp make_pair
using namespace std;
typedef pair<int, int> pii;
const int N = 5e5 + 13, L = 41;
const int inf = 1LL << 60;
int tail[N], d[N], p[N], dep[N];
vector<pii> G[N];
void dfs(int v, int par = -1){
int out = 0, son = -1;
for(auto i : G[v]){
if(i.fi != par){
d[i.fi] = d[v] + i.se;
p[i.fi] = v;
dfs(i.fi, v);
out++; son = i.fi;
}
}
tail[v] = (out == 1 ? tail[son] : v), p[tail[v]] = p[v];
}
void dfs2(int v, int par = -1){
for(auto i : G[v]){
if(i.fi != par){
if(v == tail[v]) dep[tail[i.fi]] = dep[v] + 1;
dfs2(i.fi, v);
}
}
}
struct state{
int v, dis, colour;
bool operator< (const state& o) const{
return v < o.v || v == o.v && dis < o.dis;
}
};
vector<state> qry[N];
void Init(int32_t N, int32_t A[], int32_t B[], int32_t D[]) {
for(int i = 0; i < N - 1; i++){
G[B[i]].pb({A[i], D[i]});
G[A[i]].pb({B[i], D[i]});
}
dfs(0);
dfs2(0);
}
long long Query(int32_t S, int32_t X[], int32_t T, int32_t Y[]) {
for(int j = L - 1; j >= 0; j--) qry[j].clear();
for(int j = 0; j < S; j++){
int v = X[j];
qry[dep[tail[v]]].pb({tail[v], d[v] - d[tail[v]], 0});
}
for(int j = 0; j < T; j++){
int v = Y[j];
qry[dep[tail[v]]].pb({tail[v], d[v] - d[tail[v]], 1});
}
int ans = inf;
for(int j = L - 1; j >= 0; j--){
vector<state> tmp, tmp2;
sort(qry[j].begin(), qry[j].end());
for(int i = 0; i + 1 < qry[j].size(); i++){
if(qry[j][i].v == qry[j][i + 1].v && qry[j][i].colour + qry[j][i + 1].colour == 1 && qry[j][i].dis <= 0 && qry[j][i + 1].dis <= 0)
ans = min(ans, qry[j][i + 1].dis - qry[j][i].dis);
}
for(auto k : qry[j]){
bool used1 = false, used2 = false;
if(tmp2.size() >= 1 && tmp2.back().v == k.v && tmp2.back().colour + k.colour == 1) ans = min(ans, abs(tmp2.back().dis) + abs(k.dis));
if(tmp2.size() >= 2 && tmp2[tmp2.size() - 2].v == k.v && tmp2[tmp2.size() - 2].colour + k.colour == 1) ans = min(ans, abs(tmp2[tmp2.size() - 2].dis) + abs(k.dis));
if(tmp.size() >= 1 && tmp[tmp.size() - 1].v == k.v && tmp[tmp.size() - 1].colour == k.colour){
tmp[tmp.size() - 1].dis = min(tmp[tmp.size() - 1].dis, k.dis); used1 = true;
}
if(tmp.size() >= 2 && tmp[tmp.size() - 2].v == k.v && tmp[tmp.size() - 2].colour == k.colour){
tmp[tmp.size() - 2].dis = min(tmp[tmp.size() - 2].dis, k.dis); used1 = true;
}
if(tmp2.size() >= 1 && tmp2[tmp2.size() - 1].v == k.v && tmp2[tmp2.size() - 1].colour == k.colour){
tmp2[tmp2.size() - 1].dis = min(abs(tmp2[tmp2.size() - 1].dis), abs(k.dis)); used2 = true;
}
if(tmp2.size() >= 2 && tmp2[tmp2.size() - 2].v == k.v && tmp2[tmp2.size() - 2].colour == k.colour){
tmp2[tmp2.size() - 2].dis = min(abs(tmp2[tmp2.size() - 2].dis), abs(k.dis)); used2 = true;
}
if(!used1) tmp.pb(k);
if(!used2) tmp2.pb(k);
}
if(j > 0){
for(auto k : tmp){
qry[j - 1].pb({p[k.v], k.dis + d[k.v] - d[p[k.v]], k.colour});
}
}
}
return ans;
}
