#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];
if (v && m == 0) {
return dp[i][v] = 1e18;
}
int sz = adj[i].size();
ll dp2[sz + 1][m - v + 1]{};
for (int j = sz - 1; j >= 0; j--) {
for (int k = 0; k <= m - v; k++) {
dp2[j][k] = dp2[j + 1][k] + solve(adj[i][j][0], 0) + adj[i][j][1];
if (k - 1 >= 0) {
dp2[j][k] = min(dp2[j][k], dp2[j + 1][k - 1] + solve(adj[i][j][0], 1));
}
}
}
return dp[i][v] = dp2[0][m - v];
}
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;
}
