#include "roads.h"
// #pragma GCC optimize("O3,Ofast,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
using namespace std;
#define lli long long int
#define MP make_pair
#define pb push_back
#define REP(i,n) for(int i = 0; (i) < (n); (i)++)
void fastio() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
}
const double EPS = 0.00001;
const int INF = 1e9+500;
const int M = 1e5+5;
const int ALPH = 26;
const int LGN = 25;
constexpr int MOD = 1e9+7;
int n,m,q,k;
vector<int> deg(M, 0), p(M, 0);
vector<vector<array<lli,2> > > adj(M, vector<array<lli,2> >());
vector<lli> dp[2];
void dfs(int node, int par) {
p[node] = par;
deg[node] = (int)adj[node].size();
for(auto itr = adj[node].begin(); itr!=adj[node].end();) {
auto &c = *itr;
if(c[0] == par) {
itr = adj[node].erase(itr);
continue;
}
dfs(c[0], node);
itr++;
}
}
void f(int node, int par) {
// cout<<"node:"<<node<<" par:"<<par<<endl;
if(adj[node].empty() && node) {
dp[0][node] = 0; dp[1][node] = 0;
// cout<<"node out:"<<node<<" par:"<<par<<endl;
return;
}
for(auto c : adj[node]) {
if(c[0] == par) continue;
f(c[0], node);
}
vector<lli> A1, A2;
vector<array<lli,2> > srt;
lli cost = 0;
int left = max(0, deg[node] - k);
for(int i = 0; i<adj[node].size(); i++) {
lli x = dp[1][adj[node][i][0]] + adj[node][i][1];
lli y = dp[0][adj[node][i][0]];
srt.pb({x - y, (lli)A1.size()});
A1.pb(x); A2.pb(y);
}
sort(srt.begin(), srt.end());
for(int i = 0; i<left; i++) {
cost += A1[srt[i][1]];
}
for(int i = left; i<A1.size(); i++) {
cost += min(A1[srt[i][1]], A2[srt[i][1]]);
}
dp[0][node] = cost;
left--;
if(left >= 0) dp[1][node] = cost - A1[srt[left][1]] + min(A1[srt[left][1]], A2[srt[left][1]]);
else dp[1][node] = cost;
// cout<<"dp0:"<<dp[0][node]<<" dp1:"<<dp[1][node]<<"\n";
// cout<<"node out:"<<node<<" par:"<<par<<endl;
}
lli solve() {
dp[0].assign(n + 3, 0); dp[1].assign(n + 3, 0);
f(0, 0);
return dp[0][0];
}
std::vector<long long> minimum_closure_costs(int N, std::vector<int> U,
std::vector<int> V,
std::vector<int> W) {
n = N;
lli sum = 0ll;
for(int i = 0; i<n - 1; i++) {
adj[U[i]].pb({V[i], W[i]});
adj[V[i]].pb({U[i], W[i]});
sum += W[i];
}
vector<lli> ans(n);
ans[0] = sum;
dfs(0, 0);
for(int i = 1; i<n; i++) {
k = i;
ans[i] = solve();
}
return ans;
}
