#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define mp make_pair
#define eb emplace_back
typedef long long LL;
typedef long double LD;
typedef pair<int,int> pii;
const int logn=19;
const int MAXN=500000;
int par[logn+3][MAXN+5]={},depth[MAXN+5]={};
LL jarak[MAXN+5]={};
vector <pii> node[MAXN+5];
void inisLCA(int now,int _par,int _depth,LL _jarak){
depth[now]=_depth;
jarak[now]=_jarak;
par[0][now]=_par;
for(int i=1;i<logn;i++)
par[i][now]=par[i-1][par[i-1][now]];
for(auto v:node[now])
{
if(v.fi==_par)
continue;
inisLCA(v.fi,now,_depth+1,_jarak+v.se);
}
}
void inisLCA(){
inisLCA(1,0,0,0);
}
int LCA(int u,int v){
if(depth[u]>depth[v])
swap(u,v);
int beda=depth[v]-depth[u];
for(int i=0;i<logn;i++)
{
if(beda&(1<<i))
v=par[i][v];
}
if(u==v)
return u;
for(int i=logn-1;i>=0;i--)
{
if(par[i][u]!=par[i][v])
u=par[i][u],v=par[i][v];
}
return par[0][u];
}
LL dist(int u,int v){
return jarak[u]+jarak[v]-(jarak[LCA(u,v)]<<1);
}
int parCtr[MAXN+5]={},subtree[MAXN+5]={};
int hitungSubtree(int now,int tadi){
assert(parCtr[now]==-1);
subtree[now]=1;
for(auto v:node[now]){
if(v.fi==tadi||parCtr[v.fi]!=-1)
continue;
subtree[now]+=hitungSubtree(v.fi,now);
}
return subtree[now];
}
void buatCtr(int now,int tadi){
assert(parCtr[now]==-1);
hitungSubtree(now,-1);
int target=subtree[now]>>1;
int pilihan=-1,skipAja=tadi;
bool lanjut=true;
while(lanjut)
{
lanjut=false;
for(auto v:node[now])
{
if(v.fi==skipAja||parCtr[v.fi]!=-1)
continue;
if(subtree[v.fi]>target)
{
lanjut=true;
pilihan=v.fi;
}
}
if(lanjut)
{
skipAja=now;
now=pilihan;
}
}
parCtr[now]=tadi;
for(auto v:node[now])
{
if(parCtr[v.fi]==-1)
buatCtr(v.fi,now);
}
}
void buatCtr(){
memset(parCtr,-1,sizeof(parCtr));
buatCtr(1,0);
}
void Init(int N,int A[],int B[],int D[]){
for(int i=0;i<N;i++)
{
A[i]++;B[i]++;
node[A[i]].eb(B[i],D[i]);
node[B[i]].eb(A[i],D[i]);
}
inisLCA();
buatCtr();
}
int lastReset[MAXN+5]={},kejadian=0;
LL registered[MAXN+5];
const LL INF=1000000000000000;
void ngeFix(int pos){
if(lastReset[pos]!=kejadian)
registered[pos]=INF;
lastReset[pos]=kejadian;
}
void update(int pos){
int now=pos;
while(now)
{
ngeFix(now);
registered[now]=min(registered[now],dist(now,pos));
now=parCtr[now];
}
}
LL Query(int pos){
int now=pos;
LL ret=INF;
while(now)
{
ngeFix(now);
ret=min(ret,registered[now]+dist(now,pos));
now=parCtr[now];
}
return ret;
}
LL Query(int S,int X[],int T,int Y[]){
for(int i=0;i<S;i++) X[i]++;
for(int i=0;i<T;i++) Y[i]++;
kejadian++;
for(int i=0;i<S;i++)
update(X[i]);
LL ret=INF;
for(int i=0;i<T;i++)
ret=min(ret,Query(Y[i]));
return ret;
}
