#include "race.h"
#include "bits/stdc++.h"
using namespace std;
const int N = 200001;
const int INF = 1e9;
vector < pair < int , int > > G[N];
map < pair < int , int > , int > mp;
map < pair < int , int > , bool > can;
vector < pair < int , pair < int , int > > > anc[N];
void add_edge(int u,int v,int w){
G[u].push_back({v , w});
G[v].push_back({u , w});
}
int sub[N];
bool is_rmv[N];
int gsz(int v , int p){
sub[v] = 1;
for(pair < int , int > nxt : G[v]){
int u = nxt.first;
if(u == p or is_rmv[u]) continue;
sub[v] += gsz(u , v);
}
return sub[v];
}
int find_centro(int v , int p , int need){
for(pair < int , int > nxt : G[v])
{
int u = nxt.first;
if(u == p or is_rmv[u] or sub[u] <= need / 2) continue;
return find_centro(u , v , need);
}
return v;
}
void dfs(int v , int p , int centro , int nd , int wd)
{
anc[v].push_back({centro , {wd , nd}});
if(!can[{centro , wd}]) mp[{centro , wd}] = INF;
mp[{centro , wd}] = min(mp[{centro , wd}] , nd);
can[{centro , wd}] = 1;
for(pair < int , int > nxt : G[v])
{
int u = nxt.first;
if(u != p && !is_rmv[u]) dfs(u , v , centro , nd + 1 , wd + nxt.second);
}
}
void build(int v)
{
int comp_sz = gsz(v , -1);
int centro = find_centro(v , -1 , comp_sz);
is_rmv[centro] = 1;
dfs(centro , -1 , centro , 0 , 0);
for(pair < int , int > nxt : G[centro]){
int u = nxt.first;
if(!is_rmv[u]) build(u);
}
}
int get(int v , int k)
{
int ans = INF;
for(pair < int , pair < int , int > > nxt : anc[v])
{
int centro = nxt.first;
int wg = nxt.second.first;
int ng = nxt.second.second;
int need = k - wg;
if(!can[{centro , need}]) continue;
ans = min(ans , mp[{centro , need}] + ng);
}
return ans;
}
int best_path(int N , int K , int H[][2] , int L[])
{
for(int i = 0;i < N - 1;i++) add_edge(H[i][0] , H[i][1] , L[i]);
build(0);
int ans = INF;
for(int i = 0;i < N;i++) ans = min(ans , get(i , K));
if(ans == INF) ans = -1;
return ans;
}
