#include "race.h"
#include "bits/stdc++.h"
using namespace std;
const int N = 200001;
const int INF = 1e9;
int n;
vector < pair < int , int > > G[N];
vector < pair < int , pair < int , int > > > anc[N] , arc[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}});
arc[centro].push_back({v , {wd , nd}});
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 dis(int u , int v)
{
vector < int > d(n , INF);
queue < int > q;
q.push(u);
d[u] = 0;
while(!q.empty())
{
int node = q.front();
q.pop();
for(pair < int , int > U : G[node])
{
if(d[U.first] == INF)
{
d[U.first] = d[node] + 1;
q.push(U.first);
}
}
}
return d[v];
}
int get(int v , int k)
{
int ans = INF;
for(pair < int , pair < int , int > > nxt1 : anc[v])
{
int centro = nxt1.first;
int wg = nxt1.second.first;
int ng = nxt1.second.second;
int need = k - wg;
for(pair < int , pair < int , int > > nxt2 : arc[centro])
{
int node = nxt2.first;
int wgg = nxt2.second.first;
int ngg = nxt2.second.second;
if(wgg != need) continue;
if(dis(v , node) <= dis(centro , node)) continue;
ans = min(ans , ng + ngg);
}
}
return ans;
}
int best_path(int N , int K , int H[][2] , int L[])
{
n = N;
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;
}
