#include "roads.h"
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define fi first
#define se second
#define sz(a) (int)(a.size())
#define all(a) a.begin(),a.end()
#define lb lower_bound
#define ub upper_bound
#define owo ios_base::sync_with_stdio(0);cin.tie(0);
#define INF (ll)(1e18)
#define debug(...) fprintf(stderr, __VA_ARGS__),fflush(stderr)
#define time__(d) for(long blockTime = 0; (blockTime == 0 ? (blockTime=clock()) != 0 : false);\
debug("%s time : %.4fs\n", d, (double)(clock() - blockTime) / CLOCKS_PER_SEC))
typedef long long int ll;
typedef long double ld;
typedef pair<ll,ll> PII;
typedef pair<int,int> pii;
typedef vector<vector<int>> vii;
typedef vector<vector<ll>> VII;
ll gcd(ll a,ll b){if(!b)return a;else return gcd(b,a%b);}
const int MAXN = 2e5+5;
vector<vector<pii>> g1(MAXN),g2(MAXN); //g1 is original graph,g2 is subgraph after we deleted nodes with degree<=k
vector<int>par(MAXN),szz(MAXN,1),act(MAXN); //act means whether a node is active / has degree>k
vector<ll>ans;
VII dp(2,vector<ll>(MAXN,0));
int find(int x){
if(x == par[x])return x;
else return par[x] = find(par[x]);
}
void unite(int a,int b){
a = find(a);
b = find(b);
if(a==b)return;
if(szz[a] > szz[b])swap(a,b);
par[a] = b;
szz[b]+=szz[a];
}
vector<multiset<ll>>s(MAXN);
ll query(int i,int c){
ll res = 0;
for(int x:s[i]){
if(c<=0)break;
res+=x;
c--;
}
return res;
}
void dfs(int v,int u,ll w,int k){
int need = sz(g1[v])-k;
ll cur = 0;
vector<ll>choice;
for(auto x:g2[v]){
if(x.fi != u){
dfs(x.fi,v,x.se,k);
if(dp[1][x.fi] <= dp[0][x.fi]){ //we will take this edge anyways
cur+=dp[1][x.fi];
need--;
}else{
cur+=dp[0][x.fi];
choice.pb(dp[1][x.fi]-dp[0][x.fi]);
}
}
}
dp[0][v] = dp[1][v] = INF;
sort(all(choice));
if(need<=0)dp[0][v] = cur;
if(need-1<=0)dp[1][v] = w+cur;
if(sz(s[v]) >= need)dp[0][v] = cur + query(v,need);
if(sz(s[v]) >= need-1)dp[1][v] = cur + w + query(v,need-1); //take extra edges only from inactive
ll tmp = cur+w;
for(int i=0;i<min(sz(choice),need);i++){
cur+=choice[i];
int take = need-i-1;
if(sz(s[v])>=take)dp[0][v] = min(dp[0][v],cur + query(v,take));
}
need--;
for(int i=0;i<min(sz(choice),need);i++){
tmp+=choice[i];
int take = need-i-1;
if(sz(s[v])>=take)dp[1][v] = min(dp[1][v],tmp + query(v,take));
}
}
vector<ll> minimum_closure_costs(int n, vector<int> u,vector<int>v,vector<int>w){
ans.resize(n);
for(int i=0;i<n-1;i++){
g1[u[i]].pb({v[i],w[i]});
g1[v[i]].pb({u[i],w[i]});
}
for(int i=0;i<n;i++){
for(auto x:g1[i])s[i].insert(x.se);
}
vector<int>c(n);
for(int i=0;i<n;i++){c[i] = i;par[i] = i;}
sort(all(c),[&](int x,int y){return sz(g1[x]) > sz(g1[y]);});
//sort vertex by degree and we sweep
int ptr = -1;
vector<int>vis(n);
for(int i=n-1;i>=0;i--){
while(ptr+1<n && sz(g1[c[ptr+1]]) > i){
ptr++;
int d = c[ptr];
act[d] = 1;
for(auto x:g1[d]){
if(act[x.fi]){
s[x.fi].erase(s[x.fi].find(x.se)); //these edges become active now,remove them from segtree
s[d].erase(s[d].find(x.se));
g2[x.fi].pb({d,x.se});
g2[d].pb({x.fi,x.se});
unite(x.fi,d);
}
}
}
vector<int>meet;
for(int j=0;j<=ptr;j++){
int a = find(c[j]);
if(vis[a])continue;
else{
dfs(a,-1,0,i);
meet.pb(a);
vis[a] = 1;
ans[i]+=dp[0][a];
}
}
for(int x:meet)vis[x] = 0;
}
return ans;
}
