#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, dep[N], par[N], DEG[N], deg[N];
vector<array<int, 2>> adj[N], newadj[N];
vector<int> rem[N];
void build(int i, int p, int d = 0) {
t[i] = curt++;
for (auto &[nxt, w] : adj[i]) {
if (nxt == p) continue;
build(nxt, i, d + 1);
newadj[t[i]].push_back({t[nxt], w});
}
par[t[i]] = t[p];
dep[t[i]] = d;
}
ll dp[N][2], s[N], m;
vector<ll> vals[N];
vector<ll> minimum_closure_costs(int n, vector<int> u, vector<int> v, vector<int> W) {
bool st1 = 1, st5 = 1;
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]});
st1 &= u[i] == 0;
st5 &= W[i] == 1;
}
build(0, -1);
for (int i = 0; i < n; i++) {
adj[i] = newadj[i];
}
int mx = 0;
for (int i = 0; i < n; i++) {
DEG[i] = adj[i].size() + (i != 0);
rem[DEG[i]].push_back(i);
mx = max(mx, DEG[i]);
}
if (st1) {
sort(adj[0].begin(), adj[0].end(), [&] (array<int, 2> x, array<int, 2> y) {return x[1] < y[1];});
vector<ll> ret(n);
ll s = 0;
for (int i = n - 1; i >= 0; i--) {
ret[i] = s;
if (i > 0) s += adj[0][n - 1 - i][1];
}
return ret;
} else if (st5) {
set<int> cur;
for (int i = 0; i < n; i++) cur.insert(i);
vector<ll> ret(n, 0);
for (m = 0; m < n; m++) {
for (auto j : rem[m]) cur.erase(j);
vector<int> v;
for (auto i : cur) v.push_back(i), deg[i] = DEG[i];
sort(v.begin(), v.end(), [&](int x, int y) {return dep[x] > dep[y];});
for (auto j : v) {
if (deg[j] > m) {
ret[m] += deg[j] - m;
deg[par[j]]--;
}
}
}
return ret;
}
vector<ll> ret(n);
for (m = 0; m < n; m++) {
if (m > mx) {
ret[m] = ret[m - 1];
continue;
}
for (int i = n - 1; i >= 0; i--) {
s[i] = 0;
vals[i].clear();
dp[i][0] = dp[i][1] = 0;
for (auto [nxt, w] : adj[i]) {
dp[i][0] += dp[nxt][1];
dp[i][1] += dp[nxt][1];
vals[i].push_back(- dp[nxt][1] + dp[nxt][0] + w);
}
sort(vals[i].begin(), vals[i].end());
int rem = adj[i].size() - m;
int lst = 0;
for (auto j : vals[i]) {
if (j >= 0) break;
lst++;
}
for (int j = 0; j < max(lst, rem); j++) {
dp[i][0] += vals[i][j];
}
if (m == 0) {
dp[i][1] = 1e18;
} else {
for (int j = 0; j < max(lst, rem + 1); j++) {
dp[i][1] += vals[i][j];
}
}
}
ret[m] = dp[0][0];
}
return ret;
}
