This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#ifdef MINA
#include "grader.cpp"
#endif
#include "roads.h"
using namespace std;
#define ll long long
const int N = 100'005;
int t[N], curt;
vector<array<int, 2>> adj[N];
void build(int i, int p) {
	t[i] = curt++;
	vector<array<int, 2>> newadj;
	for (auto &[nxt, w] : adj[i]) {
		if (nxt == p) continue;
		build(nxt, i);
		newadj.push_back({t[nxt], w});
	}
	adj[i] = newadj;
}
ll dp[N][2], m;
ll solve(int i, bool v) {
	if (~dp[i][v]) return dp[i][v];
	ll s = 0;
	vector<ll> vals;
	for (auto [nxt, w] : adj[i]) {
		s += solve(nxt, 1);
		vals.push_back(- solve(nxt, 1) + solve(nxt, 0) + w);
	}
	sort(vals.begin(), vals.end());
	int gud = m - v;
	if (gud < 0) {
		return dp[i][v] = 1e18;
	}
	int rem = adj[i].size() - gud;
	for (int j = 0; j < rem; j++) {
		s += vals[j];
	}
	return dp[i][v] = s;
}
vector<ll> minimum_closure_costs(int n, vector<int> u, vector<int> v, vector<int> w) {
	for (int i = 0; i < n - 1; i++) {
		adj[u[i]].push_back({v[i], w[i]});
		adj[v[i]].push_back({u[i], w[i]});
	}
	build(0, -1);
	vector<ll> ret(n);
	for (m = 0; m < n; m++) {
		for (int i = 0; i < n; i++) {
			dp[i][0] = dp[i][1] = -1;
		}
		ret[m] = solve(0, 0);
	}
	return ret;
}
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