#include <bits/stdc++.h>
#define PB push_back
#define ST first
#define ND second
//#pragma GCC optimize ("O3")
//#pragma GCC target("tune=native")
//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
//typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
using namespace std;
using ll = long long;
using pi = pair<int, int>;
using vi = vector<int>;
mt19937 rng(1190310);
const int nax = 100 * 1000 + 10, INF = 1e9;
int n, k;
set<pi>G[nax];
ll dp[nax][2];
vi ord[nax];
bool vis[nax];
int cnt[nax];
ll h[nax];
int nxt;
struct Node {
int pri = rng() % INF, val, sz = 1;
ll sum;
Node *c[2];
};
using pt = Node*;
Node T[2 * nax];
pt roots[nax];
int getsz(pt x) {
return (x == NULL ? 0 : x->sz);
}
ll getsum(pt x) {
return (x == NULL ? 0 : x->sum);
}
pt recalc(pt x) {
x->sz = getsz(x->c[0]) + getsz(x->c[1]) + 1;
x->sum = getsum(x->c[0]) + getsum(x->c[1]) + x->val;
return x;
}
pair<pt, pt>split(pt t, int kk) {
if(!t) return {t, t};
if(getsz(t->c[0]) >= kk) {
auto p = split(t->c[0], kk);
t->c[0] = p.ND;
return {p.ST, recalc(t)};
} else {
auto p = split(t->c[1], kk - getsz(t->c[0]) - 1);
t->c[1] = p.ST;
return {recalc(t), p.ND};
}
}
pair<pt, pt>split_val(pt t, int vs) {
if(!t) return {t, t};
if(t->val >= vs) {
auto p = split_val(t->c[1], vs);
t->c[1] = p.ST;
return {recalc(t), p.ND};
} else {
auto p = split_val(t->c[0], vs);
t->c[0] = p.ND;
return {p.ST, recalc(t)};
}
}
pt merge(pt a, pt b) {
if(!a || !b) return a ? a : b;
if(a->pri > b->pri) {
auto t = merge(a->c[1], b);
a->c[1] = t;
return recalc(a);
} else {
auto t = merge(a, b->c[0]);
b->c[0] = t;
return recalc(b);
}
}
void traverse(pt t) {
if(!t) return;
traverse(t->c[0]);
cout << t->val << " ";
traverse(t->c[1]);
}
void dfs(int x) {
ll sum = 0;
vis[x] = true;
vector<ll>dx = {};
for(auto [nbh, w] : G[x]) if(!vis[nbh]) {
dfs(nbh);
sum += dp[nbh][0];
if(-dp[nbh][0] + dp[nbh][1] + w > 0) dx.PB(-dp[nbh][0] + dp[nbh][1] + w);
}
sum -= h[x];
sort(dx.rbegin(), dx.rend());
dp[x][0] = dp[x][1] = sum;
int total = 0, i;
pt lft = NULL;
for(i = 0; i < (int)dx.size() && total < k - 1; ++i, ++total) {
auto p = split_val(roots[x], dx[i]);
int rem = (k - 1) - total;
if(getsz(p.ST) >= rem) {
auto p2 = split(p.ST, rem);
dp[x][1] += getsum(p2.ST);
dp[x][0] += getsum(p2.ST);
total += getsz(p2.ST);
lft = merge(lft, p2.ST);
roots[x] = merge(p2.ND, p.ND);
break;
}
dp[x][1] += getsum(p.ST);
dp[x][0] += getsum(p.ST);
total += getsz(p.ST);
lft = merge(lft, p.ST);
roots[x] = p.ND;
dp[x][1] += dx[i];
dp[x][0] += dx[i];
total++;
}
if(total < (k-1)) {
int rem = (k-1) - total;
auto p = split(roots[x], rem);
total += getsz(p.ST);
dp[x][1] += getsum(p.ST);
dp[x][0] += getsum(p.ST);
lft = merge(lft, p.ST);
roots[x] = p.ND;
}
auto p = split(roots[x], 1);
if(i < (int)dx.size()) {
dp[x][0] += max(dx[i], getsum(p.ST));
} else {
dp[x][0] += getsum(p.ST);
}
roots[x] = merge(p.ST, p.ND);
roots[x] = merge(lft, roots[x]);
//cerr << "DP: " << x << " -> " << dp[x][0] << " " << dp[x][1] << "\n";
//cout << "VALS: ";
//traverse(roots[x]);
//cout << "\n";
}
vector<ll> minimum_closure_costs(int N, vi U, vi V, vi W) {
n = N;
ll sum = 0;
for(int i = 0; i < n - 1; ++i) {
G[U[i]].insert({V[i], W[i]});
G[V[i]].insert({U[i], W[i]});
sum += W[i];
}
set<int>act = {};
for(int i = 0; i < n; ++i) {
act.insert(i);
}
for(int i = 0; i < n; ++i) {
ord[(int)G[i].size()].PB(i);
T[i].val = 0;
roots[i] = &T[i];
}
nxt = n;
vector<ll>res(n);
res[0] = sum;
ll delta = 0;
for(k = 1; k < n; ++k) {
for(auto v : ord[k]) {
act.erase(v);
for(auto [nbh, w] : G[v]) {
if(act.count(nbh)) {
delta += w;
G[nbh].erase({v, w});
cnt[nbh]++;
h[nbh] += w;
T[nxt].val = T[nxt].sum = w;
auto p = split_val(roots[nbh], w);
roots[nbh] = merge(p.ST, &T[nxt]);
roots[nbh] = merge(roots[nbh], p.ND);
nxt++;
}
}
}
ll s = 0;
for(auto v : act) {
if(!vis[v]) {
dfs(v);
s += dp[v][0];
}
}
for(auto v : act)
vis[v] = false;
res[k] = (sum - (s + delta));
}
return res;
}
//int main() {
//ios_base::sync_with_stdio(0);
//cin.tie(0);
//auto vec = minimum_closure_costs(4, {0, 2, 0}, {1, 0, 3}, {5, 10, 5});
//auto vec = minimum_closure_costs(5, {0, 0, 0, 2}, {1, 2, 3, 4}, {1, 4, 3, 2});
//cin >> n;
//vi u(n-1), v(n-1), w(n-1);
//for(int i = 0; i < n-1; ++i) cin >> u[i] >> v[i] >> w[i];
//auto vec = minimum_closure_costs(n, u, v, w);
//for(auto x : vec) cout << x << " ";
//}
