#include "roads.h"
#include <bits/stdc++.h>
std::vector<long long> minimum_closure_costs(int N, std::vector<int> U,
std::vector<int> V,
std::vector<int> W) {
std::vector<std::vector<std::pair<int, int>>> adj(N);
long long tot = 0;
for (int i = 0; i < N - 1; i++) {
int u = U[i], v = V[i], w = W[i];
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
tot += w;
}
auto solve = [&](int k) -> long long {
std::vector<std::array<long long, 2>> dp(N, {-1, -1});
auto dfs = [&](auto self, int u, int p, int s) {
if (dp[u][s] != -1) return dp[u][s];
std::vector<std::pair<int, std::pair<int, int>>> options;
for (auto [v, w] : adj[u]) {
if (v == p) continue;
self(self, v, u, 0);
self(self, v, u, 1);
options.emplace_back(dp[v][1] - (dp[v][0] + w), std::make_pair(v, w));
}
std::sort(options.begin(), options.end());
int rem = k - s;
long long ans = 0;
for (int i = 0; i < (int) options.size(); i++) {
int v = options[i].second.first;
int w = options[i].second.second;
if (i < rem) {
ans += dp[v][1];
} else {
ans += dp[v][0] + w;
}
}
return dp[u][s] = ans;
};
return dfs(dfs, 0, -1, 0);
};
std::vector<long long> res(N);
res[0] = tot;
res[N - 1] = 0;
for (int i = N - 2; i >= 1; i--) {
res[i] = solve(i);
}
return res;
}
