#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vll = vector<ll>;
using vvl = vector<vll>;
using pll = pair<ll,ll>;
using vpl = vector<pll>;
using vvp = vector<vpl>;
using vi = vector<int>;
#define f first
#define s second
#define pb push_back
#define all(v) v.begin(),v.end()
vll dp, dp1;
vvp g, gr;vvl sm, rm;
void dfs(ll cur, ll pr, ll k){
priority_queue<ll,vll,greater<ll>> pq;
for(auto [i,e]: g[cur]){
if(i!=pr){
dfs(i,cur,k);
dp1[cur]+=dp[i];
pq.push(dp1[i]-dp[i]+e);
}
}
ll cnt=0;
while(!pq.empty() && (pq.top()<0 || g[cur].size()-cnt-1>k)){
auto v = pq.top();
pq.pop();
dp1[cur]+=v;
cnt++;
}
dp[cur]=dp1[cur];
while(!pq.empty() && (pq.top()<0 || g[cur].size()-cnt>k)){
auto v = pq.top();
pq.pop();
dp[cur]+=v;
cnt++;
}
}
void dfs2(ll cur, ll pr, ll k){
priority_queue<ll,vll,greater<ll>> pq;
for(auto [i,e]: gr[cur]){
if(i!=pr){
dfs2(i,cur,k);
dp1[cur]+=dp[i];
pq.push(dp1[i]-dp[i]+e);
}
}
ll cnt=g[cur].size()-k-1, t=0;
while(!pq.empty() && (pq.top()<0 || cnt>0)){
auto v = pq.top();
pq.pop();
ll nx = upper_bound(all(sm[cur]),v)-sm[cur].begin();
nx = min(t+cnt,nx);
cnt -= (nx-t);
dp1[cur] += rm[cur][nx]-rm[cur][t];
t=nx;
if(cnt>0 || v<0){
dp1[cur]+=v;
cnt--;
}
}
cnt++;
dp[cur]=dp1[cur];
while(!pq.empty() && (pq.top()<0 || cnt>0)){
auto v = pq.top();
pq.pop();
ll nx = upper_bound(all(sm[cur]),v)-sm[cur].begin();
nx = min(t+cnt,nx);
cnt -= (nx-t);
dp[cur] += rm[cur][nx]-rm[cur][t];
t=nx;
if(cnt>0 || v<0){
dp[cur]+=v;
cnt--;
}
}
}
std::vector<long long> minimum_closure_costs(int n, vi u, vi v, vi w) {
gr=g = vvp(n);
vll ans(n);
ll B = 2;
rm=sm = vvl(n);
B = min<ll>(B,n-1);
for(ll i = 0; i < n-1; ++i){
ans[0]+=w[i];
g[u[i]].pb({v[i],w[i]});
g[v[i]].pb({u[i],w[i]});
}
vll las(n-1,1);
for(ll i = 1; i <= B; ++i){
dp=dp1=vll(n);
dfs(0,0,i);
ans[i]=dp[0];
}
vll big;
for(ll i = 0; i < n; ++i){
if(g[i].size()>B){
big.pb(i);
for(auto [j,v]: g[i]){
if(g[j].size()>B){
gr[i].pb({j,v});
}
else sm[i].pb(v);
}
sort(all(sm[i]));
sm[i].pb(1e10);
rm[i]={0};
for(ll j = 0; j < sm[i].size(); ++j){
rm[i].pb(rm[i][j]+sm[i][j]);
}
}
}
for(ll i = B+1; i < n; ++i){
for(ll j: big){
dp[j]=-1;
dp1[j]=0;
}
for(ll j: big){
if(dp[j]==-1){dfs2(j,j,i);ans[i]+=dp[j];}
}
}
return ans;
}
// int main() {
// int N;
// assert(1 == scanf("%d", &N));
// vi U(N - 1), V(N - 1), W(N - 1);
// for (int i = 0; i < N - 1; ++i) {
// assert(3 == scanf("%d %d %d", &U[i], &V[i], &W[i]));
// }
// std::vector<long long> closure_costs = minimum_closure_costs(N, U, V, W);
// for (int i = 0; i < static_cast<int>(closure_costs.size()); ++i) {
// if (i > 0) {
// printf(" ");
// }
// printf("%lld",closure_costs[i]);
// }
// printf("\n");
// return 0;
// }
