#include "roads.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define all(c) ((c).begin()), ((c).end())
#define sz(x) ((int)(x).size())
int MAXW;
const ll INF = 1LL << 50;
inline int get(const vector <int> &V, int k){
int ans = 0;
int total = accumulate(V.begin(), V.end(), 0);
k = total - k;
for(int i = 0;i < sz(V);++i){
int need = min(k, V[i]);
k -= need;
ans += need * i;
if(k <= 0) break;
}
return ans;
}
std::vector<long long> minimum_closure_costs(int n, vector<int> a, vector<int> b, vector<int> w) {
ll W = 0;
vector<vector<int>> adj(n);
for (int i = 0; i + 1 < n; i++) {
adj[a[i]].push_back(i);
adj[b[i]].push_back(i);
W += w[i];
MAXW = max(MAXW, w[i]);
}
vector<int> perm(n);
iota(all(perm), 0);
sort(all(perm), [&](int i, int j) {return sz(adj[i]) > sz(adj[j]);});
vector<vector<int>> nodes(n);
vector<vector<int>> D(n, vector <int>(MAXW + 1, 0));
for (int i = 0; i < n; i++) {
sort(all(adj[i]), [&](int j, int k) {
int u = a[j] ^ b[j] ^ i;
int v = a[k] ^ b[k] ^ i;
return sz(adj[u]) > sz(adj[v]);
});
nodes[sz(adj[i])].push_back(i);
}
vector<ll> answers(n); answers[0] = W;
vector<bool> vis(n);
vector<vector<ll>> dp(n, vector<ll>(2));
for (int k = 1; k < n; k++) {
for (int s : nodes[k]) {
// activate
for (int ind : adj[s]) {
int v = a[ind] ^ b[ind] ^ s;
D[v][w[ind]]++;
}
}
for (int u : perm) {
vis[u] = false;
if (sz(adj[u]) <= k) break;
}
function<void(int, int)> dfs = [&](int s, int p) {
vis[s] = true;
vector<ll> vals;
ll sum = 0;
for (int ind : adj[s]) {
int v = a[ind] ^ b[ind] ^ s;
if (v == p) continue;
if (sz(adj[v]) <= k) break;
dfs(v, s);
sum += dp[v][0] + w[ind];
vals.push_back(dp[v][1] - w[ind] - dp[v][0]);
}
sort(all(vals));
dp[s][0] = dp[s][1] = INF;
for (int i = 0; i <= sz(vals) && i <= k; i++) {
dp[s][0] = min(dp[s][0], sum + get(D[s], k - i));
if (i < k) {
dp[s][1] = min(dp[s][1], sum + get(D[s], k - 1 - i));
}
if (i < sz(vals)) sum += vals[i];
}
};
answers[k] = 0;
for (int u : perm) {
if (sz(adj[u]) <= k) break;
if (!vis[u]) {
dfs(u, u);
answers[k] += dp[u][0];
}
}
}
return answers;
}
