#include "roads.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<int,int>
#define fi first
#define se second
const ll inf = 1e18;
struct Segtree{
int sz;
vector<ll> tree;
vector<int> cnt;
vector<pii> com;
Segtree(){}
void add(pii val){
com.push_back(val);
}
void build(int l,int r,int id){
if(l==r){
tree[id]=com[l-1].fi;
cnt[id]=1;
return;
}
int mid=(l+r)>>1;
build(l,mid,id<<1);build(mid+1,r,id<<1|1);
tree[id]=tree[id<<1]+tree[id<<1|1];
cnt[id]=cnt[id<<1]+cnt[id<<1|1];
}
void update(int l,int r,int id,int p){
if(l==r){
tree[id]=cnt[id]=0;
return;
}
int mid=(l+r)>>1;
if(p<=mid) update(l,mid,id<<1,p);
else update(mid+1,r,id<<1|1,p);
tree[id]=tree[id<<1]+tree[id<<1|1];
cnt[id]=cnt[id<<1]+cnt[id<<1|1];
}
ll query(int l,int r,int id,int k){
if(l==r) return (k>=1)*tree[id];
int mid=(l+r)>>1;
if(cnt[id<<1]<k) return tree[id<<1]+query(mid+1,r,id<<1|1,k-cnt[id<<1]);
else return query(l,mid,id<<1,k);
}
void build(){
sort(com.begin(),com.end(),greater<pii>());
sz=(int)com.size();
tree.assign(4*sz,0);
cnt.assign(4*sz,0);
build(1,sz,1);
}
void del(pii x){
int pos=lower_bound(com.begin(),com.end(),x,greater<pii>())-com.begin()+1;
update(1,sz,1,pos);
}
ll query(int k){
return query(1,sz,1,k);
}
};
std::vector<ll> minimum_closure_costs(int N, vector<int> U,
vector<int> V,
vector<int> W) {
vector<ll> res(N),total(N);
vector<vector<pii>> edge(N),adj(N);
vector<vector<int>> pos(N);
vector<Segtree> ST(N);
vector<bool> add(N,false),vis(N,false);
for(int i=0;i<N-1;i++){
edge[U[i]].push_back({V[i],W[i]});
edge[V[i]].push_back({U[i],W[i]});
}
for(int i=0;i<N;i++){
pos[(int)edge[i].size()].push_back(i);
for(auto [v,w]:edge[i]) ST[i].add({w,v}),total[i]+=w;
ST[i].build();
}
vector<int> cc;
vector<array<ll,2>> dp(N);
for(int k=N-1;k>=0;k--){
for(int u:pos[k]){
cc.push_back(u);
for(auto [v,w]:edge[u]){
total[v]-=w;
ST[v].del({w,u});
if(add[v]){
adj[u].push_back({v,w});
adj[v].push_back({u,w});
}
}
add[u]=true;
}
function<void(int)> dfs = [&](int u){
int C=0;vis[u]=true;
dp[u][0]=dp[u][1]=inf;
ll num=total[u];
vector<ll> val;
for(auto [v,w]:adj[u]){
if(vis[v]){C=w;continue;}
dfs(v);num+=dp[v][0];
if(dp[v][0]>dp[v][1]) val.push_back(dp[v][0]-dp[v][1]);
}
sort(val.begin(),val.end(),greater<ll>());
ll cur=num;
for(int i=0;i<=(int)val.size();i++){
if(i) cur-=val[i-1];
if(i<=k) dp[u][0]=min(dp[u][0],cur-ST[u].query(k-i)+C);
if(i<k) dp[u][1]=min(dp[u][1],cur-ST[u].query(k-1-i));
}
};
for(int u:cc) vis[u]=false;
for(int u:cc) if(!vis[u]){
dfs(u);
res[k]+=min(dp[u][0],dp[u][1]);
}
}
return res;
}
