#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include "factories.h"
using namespace std;
using namespace __gnu_pbds;
#define ff first
#define ss second
#define ll int64_t
#define ld long double
#define nl cout<<"\n"
#define all(v) v.begin(),v.end()
#define mset(a,v) memset((a),(v),sizeof(a))
#define forn(i,a,b) for(int64_t i=int64_t(a);i<int64_t(b);++i)
#define forb(i,a,b) for(int64_t i=int64_t(a);i>=int64_t(b);--i)
#define fastio() ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define mod 1'000'000'007
#define mod2 998'244'353
#define inf 1'000'000'000'000'007
#define pi 3.14159265358979323846
template<class key,class cmp=std::less<key>>
using ordered_set=tree<key,null_type,cmp,rb_tree_tag,tree_order_statistics_node_update>;
template<class L,class R> ostream& operator<<(ostream& out,pair<L,R> &p) {return out<<"("<<p.ff<<", "<<p.ss<<")";}
template<class T> ostream& operator<<(ostream& out,vector<T> &v) {out<<"[";for(auto it=v.begin();it!=v.end();++it){if(it!=v.begin())out<<", ";out<<*it;}return out<<"]";}
template<class T> ostream& operator<<(ostream& out,deque<T> &v) {out<<"[";for(auto it=v.begin();it!=v.end();++it){if(it!=v.begin())out<<", ";out<<*it;}return out<<"]";}
template<class T> ostream& operator<<(ostream& out,set<T> &s) {out<<"{";for(auto it=s.begin();it!=s.end();++it){if(it!=s.begin())out<<", ";out<<*it;}return out<<"}";}
template<class L,class R> ostream& operator<<(ostream& out,map<L,R> &m) {out<<"{";for(auto it=m.begin();it!=m.end();++it){if(it!=m.begin())out<<", ";out<<*it;}return out<<"}";}
void dbg_out() {cerr<<"]\n";}
template<typename Head,typename... Tail>
void dbg_out(Head H,Tail... T) {cerr<<H;if(sizeof...(Tail))cerr<<", ";dbg_out(T...);}
#ifdef LOCAL
#define dbg(...) cerr<<"["<<#__VA_ARGS__<<"] = [",dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif
//---------------------------------mars4---------------------------------
vector<vector<ll>> v;
vector<vector<pair<ll,ll>>> ve;
vector<ll> len;
vector<ll> best;
vector<ll> updated;
void dfs(ll cur,ll prev,ll d)
{
len[cur]=d;
for(auto [i,w]:ve[cur])
{
if(i!=prev)
{
dfs(i,cur,d+w);
}
}
}
class LCA
{
ll n;
ll N;
ll K;
void dfs(ll cur,ll prev,vector<vector<ll>> &v)
{
ind[cur]=(ll)euler.size();
euler.push_back(cur);
euler_depth.push_back(depth[cur]);
for(ll i:v[cur])
{
if(i!=prev)
{
depth[i]=depth[cur]+1;
dfs(i,cur,v);
euler.push_back(cur);
euler_depth.push_back(depth[cur]);
}
}
}
void build()
{
N=(ll)euler_depth.size();
K=64-__builtin_clzll(N);
st=vector<vector<ll>>(N,vector<ll>(K));
logN=vector<ll>(N+1);
for(int i=2;i<=N;i++)
{
logN[i]=logN[i/2]+1;
}
for(int i=1;i<N;i++)
{
st[i][0]=i;
}
for(int j=1;j<=K;j++)
{
for(int i=0;i+(1ll<<j)<=N;i++)
{
if(euler_depth[st[i][j-1]]<euler_depth[st[i+(1ll<<(j-1))][j-1]])
{
st[i][j]=st[i][j-1];
}
else
{
st[i][j]=st[i+(1ll<<(j-1))][j-1];
}
}
}
}
public:
vector<ll> euler;
vector<ll> ind;
vector<ll> depth;
vector<ll> euler_depth;
vector<vector<ll>> st;
vector<ll> logN;
void init(vector<vector<ll>> &v,ll root=0)
{
ll n=(ll)v.size();
ind=vector<ll>(n);
depth=vector<ll>(n);
dfs(root,-1,v);
build();
}
ll lca(ll u,ll v)
{
if(ind[u]>ind[v])
{
swap(u,v);
}
ll l=ind[u];
ll r=ind[v];
ll j=logN[r-l+1];
if(euler_depth[st[l][j]]<euler_depth[st[r-(1ll<<j)+1][j]])
{
return euler[st[l][j]];
}
else
{
return euler[st[r-(1ll<<j)+1][j]];
}
}
ll dist(ll u,ll v)
{
return len[u]+len[v]-2*len[lca(u,v)];
}
};
class CentroidDecomposition
{
ll N;
void dfs_sz(vector<vector<ll>> &v,ll cur,ll prev)
{
sz[cur]=1;
for(ll i:v[cur])
{
if(i!=prev and !visited[i])
{
dfs_sz(v,i,cur);
sz[cur]+=sz[i];
}
}
}
ll get_centroid(vector<vector<ll>> &v,ll cur,ll prev,ll tot_sz)
{
for(ll i:v[cur])
{
if(i!=prev and !visited[i] and sz[i]>tot_sz/2)
{
return get_centroid(v,i,cur,tot_sz);
}
}
return cur;
}
void build(vector<vector<ll>> &v,ll cur,ll prev)
{
dfs_sz(v,cur,prev);
ll centroid=get_centroid(v,cur,prev,sz[cur]);
visited[centroid]=true;
parent[centroid]=prev;
for(ll i:v[centroid])
{
if(!visited[i])
{
build(v,i,centroid);
}
}
}
public:
vector<ll> parent;
vector<ll> sz;
vector<bool> visited;
void init(vector<vector<ll>> &v)
{
N=(ll)v.size();
parent=vector<ll>(N);
sz=vector<ll>(N);
visited=vector<bool>(N);
build(v,0,-1);
}
};
LCA lca;
CentroidDecomposition cd;
void update(ll node,ll cur)
{
while(cur!=-1)
{
updated.push_back(cur);
best[cur]=min(best[cur],lca.dist(node,cur));
cur=cd.parent[cur];
}
}
ll query(ll node,ll cur)
{
ll res=inf;
while(cur!=-1)
{
res=min(res,lca.dist(node,cur)+best[cur]);
cur=cd.parent[cur];
}
return res;
}
void Init(int N,int A[],int B[],int D[])
{
v=vector<vector<ll>>(N);
ve=vector<vector<pair<ll,ll>>>(N);
len=vector<ll>(N);
best=vector<ll>(N,inf);
forn(i,0,N-1)
{
v[A[i]].push_back({B[i]});
v[B[i]].push_back({A[i]});
ve[A[i]].push_back({B[i],D[i]});
ve[B[i]].push_back({A[i],D[i]});
}
dfs(0,-1,0);
lca.init(v);
cd.init(v);
}
long long Query(int S,int X[],int T,int Y[])
{
forn(i,0,S)
{
update(X[i],X[i]);
}
ll res=inf;
forn(i,0,T)
{
res=min(res,query(Y[i],Y[i]));
}
for(ll i:updated)
{
best[i]=inf;
}
updated.clear();
return res;
}
