#include<bits/stdc++.h>
#include "roads.h"
#define MAXN 100007
using namespace std;
const long long inf=1e10;
int n,a,b,k,sz[MAXN];
long long sum;
vector<int> toadd[MAXN];
vector< pair<int,int> > v[MAXN],g[MAXN];
long long dp[MAXN][2];
int li[MAXN][2],tim;
struct edges{
vector<int> s;
void add(int x){
s.push_back(x);
sort(s.begin(),s.end());
}
void rem(int x){
for(int i=0;i<s.size();i++){
if(s[i]==x){
swap(s[i],s[s.size()-1]);
s.pop_back(); break;
}
}
sort(s.begin(),s.end());
}
}bonus[MAXN];
long long ff(int x,int p,bool par){
if(li[x][par]==tim)return dp[x][par];
li[x][par]=tim;
dp[x][par]=0;
vector<long long> s;
for(int i=0;i<v[x].size();i++){
if(v[x][i].first==p){
if(par)dp[x][par]+=v[x][i].second;
continue;
}
s.push_back(ff(v[x][i].first,x,true)-ff(v[x][i].first,x,false));
dp[x][par]+=ff(v[x][i].first,x,false);
}
sort(s.begin(),s.end());
int pt=0;
for(int i=0;i<sz[x]-k-par-pt or (i<int(s.size()) and s[i]<0);i++){
if(s.empty() or (pt<bonus[x].s.size() and bonus[x].s[pt]<s[i])){
dp[x][par]+=bonus[x].s[pt]; pt++; i--;
}else{
dp[x][par]+=s[i];
}
}
return dp[x][par];
}
bool in[MAXN];
vector<int> roots;
vector<long long> minimum_closure_costs(int N,vector<int> U,vector<int> V,vector<int> W){
n=N;
for(int i=1;i<=n-1;i++){
a=U[i-1]; b=V[i-1];
a++; b++;
bonus[a].add(W[i-1]);
bonus[b].add(W[i-1]);
sz[a]++; sz[b]++;
g[a].push_back({b,W[i-1]});
g[b].push_back({a,W[i-1]});
sum+=W[i-1];
}
for(int i=1;i<=n;i++){
toadd[bonus[i].s.size()-1].push_back(i);
}
vector<long long> res;
for(int i=n-1;i>=1;i--){
for(int f:toadd[i]){
for(pair<int,int> k:g[f]){
if(!in[k.first])continue;
v[f].push_back({k.first,k.second});
v[k.first].push_back({f,k.second});
bonus[f].rem(k.second);
bonus[k.first].rem(k.second);
}
in[f]=true;
roots.push_back(f);
}
long long curr=0;
tim++; k=i;
for(int f:roots){
if(li[f][0]==tim)continue;
curr+=ff(f,0,0);
}
res.push_back(curr);
}
res.push_back(sum);
reverse(res.begin(),res.end());
return res;
}
/*int main(){
//vector<long long> s=minimum_closure_costs(5, {0, 0, 0, 2}, {1, 2, 3, 4}, {1, 4, 3, 2});
//vector<long long> s=minimum_closure_costs(4, {0, 2, 0}, {1, 0, 3}, {5, 10, 5});
for(long long i:s)cout<<i<<" ";
return 0;
}*/
