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 "roads.h"
#include <vector>
#include <bits/stdc++.h>
using namespace std;
constexpr int NMAX = 100005;
typedef long long LL;
constexpr LL INF = 1LL * 1e15;
struct muchie {
    int x, y;
    LL cost;
};
muchie E[NMAX];
vector <int> G[NMAX];
LL dp[NMAX][2];
LL aux[NMAX];
void Dfs (int k, int Node, int dad = -1) {
    for (auto it : G[Node]) {
        int to = (E[it].x == Node ? E[it].y : E[it].x);
        if (to == dad) continue;
        Dfs(k, to, Node);
    }
    for (int i = 0; i <= k; ++ i )
        aux[i] = 0;
    aux[0] = 0;
    int grad = 0;
    for (auto it : G[Node]) {
        int to = (E[it].x == Node ? E[it].y : E[it].x);
        if (to == dad) continue;
        ++ grad;
        aux[grad] = aux[grad-1] + dp[to][0];
        for (int cnt = min(grad-1, k); cnt >= 0; -- cnt ) {
            ///       elimin muchia Node -> to;  NU elimin muchia Node -> to
            aux[cnt] = aux[cnt] + dp[to][1];
            if (cnt > 0) aux[cnt] = min(aux[cnt], aux[cnt-1] + dp[to][0]);
        }
    }
    dp[Node][0] = INF;
    dp[Node][1] = INF;
    if (k > 0) dp[Node][0] = aux[min(grad, k-1)];
    if (dad == -1)
        dp[Node][1] = aux[min(grad, k)];
    for (auto it : G[Node]) {
        int to = (E[it].x == Node ? E[it].y : E[it].x);
        if (to != dad) continue;
        dp[Node][1] = aux[min(grad, k)] + E[it].cost;
        break;
    }
}
std::vector<long long> minimum_closure_costs(int N, std::vector<int> U,
                                             std::vector<int> V,
                                             std::vector<int> W) {
    for (int i = 1; i < N; ++ i ) {
        E[i] = {U[i-1], V[i-1], 1LL * W[i-1]};
        G[U[i-1]].push_back(i);
        G[V[i-1]].push_back(i);
    }
    vector <LL> ans;
    for (int k = 0; k < N; ++ k ) {
        Dfs(k, 0);
        ans.push_back(dp[0][1]);
    }
    return ans;
}
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