#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 up[19][N];
int dep[N];
void DFS(int v , int p)
{
if(v > 0) dep[v] = dep[p] + 1;
up[0][v] = p;
for(int i = 1;i < 19;i++) up[i][v] = up[i - 1][up[i - 1][v]];
for(pair < int , int > nxt : G[v]){
int u = nxt.first;
if(u != p) DFS(u , v);
}
}
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 LCA(int u , int v)
{
if(dep[u] < dep[v]) swap(u , v);
int dif = dep[u] - dep[v];
for(int i = 18;i >= 0;i--)
{
if((1 << i) & dif) u = up[i][u];
}
if(u == v) return u;
for(int i = 18;i >= 0;i--)
{
if(up[i][u] != up[i][v])
{
u = up[i][u];
v = up[i][v];
}
}
return up[0][u];
}
int dis(int u , int v)
{
int lca = LCA(u , v);
return (dep[v] - dep[lca]) + (dep[u] - dep[lca]);
}
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 , centro) + dis(centro , node) != dis(v , 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]);
DFS(0 , -1);
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;
}
