#include "closing.h"
#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
#define pb push_back
#define F first
#define pii pair<int,int>
#define all(a) a.begin(),a.end()
#define S second
#define sz(a) (int)a.size()
#define rep(i , a , b) for(int i = (a) ; i <= (b) ; i++)
#define per(i , a , b) for(int i = (a) ; i >= (b) ; i--)
#define ld double
#define ll long long
using namespace std ;
const int maxn = 5e5 + 10 ,s = 1000 , inf = 1e9 , mod = 998244353;
int par[maxn] , r[maxn] , ma[maxn] , mark[maxn] , mb[maxn] ;
ll dis[maxn] , a[maxn] , b[maxn] ;
vector <pii> G[maxn] ;
void dfs(int v){
for(auto[u,w] : G[v]){
if(u == par[v])continue ;
par[u] = v;
dfs(u) ;;
}
}
void dist(int v, int p = -1){
for(auto [u,w] : G[v]){
if(u == p)continue ;
dis[u ]= dis[v] + w ;
dist(u , v);
}
}
void dfs2(int v, int p =-1 ){
mark[v] =1 ;
for(auto[u,w] : G[v]){
if(mark[u] == 1)continue ;
r[u] = r[v];
dfs2(u ,v );
}
}
int max_score(int n, int x, int y, long long K,std::vector<int> U, std::vector<int> V, std::vector<int> W){
rep(i , 0 ,n)G[i].clear() ;
rep(i , 0 , n-2){
G[V[i]].pb({U[i],W[i]});
G[U[i]].pb({V[i] , W[i]}) ;
}
dis[x] =0 ;
dist(x);
rep(i ,0, n-1){
a[i] = dis[i] ;
}
dis[y] = 0;
dist(y) ;
rep(i ,0 ,n-1){
b[i] = dis[i] ;
}
par[x] = -1 ;
dfs(x) ;
vector <int >vec ;
int f = y ;
while(f!=-1){
vec.pb(f);
f = par[f] ;
}
rep(i , 0 , n)mark[i] =0 ;
for(int x : vec)mark[x] =1 ;
for(int x : vec){
r[x] = x ;
dfs2(x) ;
}
reverse(all(vec)) ;
int ans =0 ;
rep(i , 0 ,n)ma[i] = mb[i] =0 ;
rep(i , 0 ,sz(vec)-1){
ma[vec[i]] = 1;
per(j , sz(vec)-1 , 0){
mb[vec[j]] =1 ;
ll sm = K ; int ted= 0 ;;
vector<ll> az;
rep(k , 0 ,n-1){
if(r[k] == k){
ll mx = 0;
if(ma[k] == 1){ted++;mx =max(mx , a[k]);}
if(mb[k] == 1){ted++;mx =max(mx , b[k]);}
sm -= mx ;
}else{
if(ma[r[k]]==1)az.pb(a[k]);
if(mb[r[k]]==1)az.pb(b[k]);
}
}
if(sm < 0)continue ;
sort(all(az));
rep(i , 0 ,sz(az)-1){
if(sm < az[i])break ;
sm -= az[i] ;
ted++ ;
}
ans = max(ans , ted) ;
}
rep(j ,0 , sz(vec)-1)mb[vec[j]] =0 ;
}
return ans;
}
