#include<bits/stdc++.h>
#define f first
#define s second
#define ll long long
#define pb push_back
#define pii pair<int,int>
#define pll pair<ll,ll>
#define sz(x) (int)x.size()
#define all(x) x.begin(),x.end()
#define vi vector<int>
#define vvi vector<vi>
#define vll vector<ll>
using namespace std;
const int mxn=1e5+5;
vector<pii>g[mxn],gr[mxn];int d[mxn]{0};ll s1[mxn]{0};
vll fw[mxn][2],val[mxn];
void add(int i,ll x,int j){
int id=upper_bound(val[i].begin(),val[i].end(),x)-val[i].begin();
for(;id<fw[i][0].size();id+=id&-id)fw[i][0][id]+=j,fw[i][1][id]+=x*j;
}
pll qr(int i,ll x,ll rs=0,ll rs2=0){
int id=upper_bound(val[i].begin(),val[i].end(),x)-val[i].begin();
for(;id;id-=id&-id)rs+=fw[i][0][id],rs2+=fw[i][1][id];
return {rs,rs2};
}
ll dp[mxn][2]{0};
vi node;bool use[mxn]{0};
void solve(int u,int p,int k){
vector<ll>v0;int pr=-1;ll sm=0;use[u]=1;
for(auto v:gr[u]){
if(v.f==p){pr=v.s;continue;}
solve(v.f,u,k);v0.pb(dp[v.f][0]-dp[v.f][1]);sm+=dp[v.f][1];
}dp[u][0]=s1[u]+sm+(pr==-1?0:pr);if(pr!=-1)v0.pb(-pr);
sort(v0.begin(),v0.end());
ll l=-1e15,r=1e15;
while(l<r){
ll m=(l+r)>>1;
int id1=qr(u,m).f;
int id2=upper_bound(v0.begin(),v0.end(),m)-v0.begin();
if(id1+id2>=k)r=m;
else l=m+1;
}pll x=qr(u,l);dp[u][0]+=x.s;int mem=0;
for(int i=0;i<v0.size();i++)if(v0[i]<=l)mem=i+1,dp[u][0]+=v0[i];
dp[u][0]-=l*(mem+x.f-k);if(pr==-1)return;
for(int i=0;i<v0.size();i++)if(v0[i]==-pr)mem=i;
swap(v0[mem],v0.back());v0.pop_back();dp[u][1]=s1[u]+sm+pr;sort(v0.begin(),v0.end());
l=-1e15,r=1e15;
while(l<r){
ll m=(l+r)>>1;
int id1=qr(u,m).f;
int id2=upper_bound(v0.begin(),v0.end(),m)-v0.begin();
if(id1+id2>=k)r=m;
else l=m+1;
}x=qr(u,l);dp[u][1]+=x.s;mem=0;
for(int i=0;i<v0.size();i++)if(v0[i]<=l)mem=i+1,dp[u][1]+=v0[i];
dp[u][1]-=l*(mem+x.f-k);
}
vll minimum_closure_costs(int N,vi U,vi V,vi W){vll ans(N,0);ll res=0,tt=0;
for(int i=0;i<N-1;i++)g[U[i]].pb({V[i],W[i]}),g[V[i]].pb({U[i],W[i]}),d[U[i]]++,d[V[i]]++,tt+=W[i];
for(int i=0;i<N;i++)for(auto v:g[i])s1[i]+=v.s,val[i].pb(-v.s);
for(int i=0;i<N;i++){
sort(val[i].begin(),val[i].end()),fw[i][0].resize(val[i].size()+2),fw[i][1].resize(val[i].size()+2);
for(auto it : val[i])add(i,it,1);
}
vector<pii>ed;for(int i=0;i<N-1;i++)ed.pb({min(d[U[i]],d[V[i]]),i});sort(ed.begin(),ed.end());
priority_queue<pii>pq;for(int i=0;i<N;i++)pq.push({d[i],i});
for(int k=N-1;k>=1;k--){
while(!pq.empty()&&pq.top().f>k)node.pb(pq.top().s),pq.pop();
while(!ed.empty()&&ed.back().f>k){
int i=ed.back().s;ed.pop_back();
gr[U[i]].pb({V[i],W[i]});gr[V[i]].pb({U[i],W[i]});
s1[U[i]]-=W[i];s1[V[i]]-=W[i];add(U[i],-W[i],-1);
add(V[i],-W[i],-1);
}
for(auto it:node)if(!use[it])solve(it,it,k),res+=dp[it][0];
for(auto it:node)use[it]=0,dp[it][0]=dp[it][1]=0;
ans[k]=res;res=0;
}ans[0]=tt;
return ans;
}
