#include "closing.h"
#include<bits/stdc++.h>
#define f0r(i,n) for(ll i = 0;i<n;i++)
#define FOR(i, k, n) for(int i = k;i<n;i++)
#define pb push_back
#define vi vector<long long int>
#define ll long long int
#define mp make_pair
using namespace std;
int max_score(int N, int X, int Y, long long K,
std::vector<int> U, std::vector<int> V, std::vector<int> W)
{
vector<pair<ll,ll>> adj[N];
f0r(i, N-1){
adj[U[i]].pb({V[i], W[i]});
adj[V[i]].pb({U[i], W[i]});
}
vector<vector<ll>>dist(N, vector<ll>(2, 4e18));
vector<bool>vis(N, 0);
queue<int>q;
q.push(X);
vis[X] = 1;
dist[X][0] = 0;
while(!q.empty()){
int c = q.front();
q.pop();
for(auto u : adj[c]){
if(vis[u.first])continue;
vis[u.first] = 1;
dist[u.first][0] = min(dist[u.first][0], dist[c][0] + u.second);
q.push(u.first);
}
}
f0r(i,N)vis[i] = 0;
vis[Y] = 1;
dist[Y][1] = 0;
q.push(Y);
while(!q.empty()){
int c = q.front();
q.pop();
for(auto u : adj[c]){
if(vis[u.first])continue;
vis[u.first] = 1;
dist[u.first][1] = min(dist[u.first][1], dist[c][1] + u.second);
q.push(u.first);
}
}
if(dist[Y][0] > 2 * K){
vector<ll> dists;
f0r(i, N){
dists.pb(min(dist[i][0], dist[i][1]));
}
sort(dists.begin(), dists.end());
int ans = 0;
ll s = 0;
f0r(i, N){
if(s + dists[i] > K)break;
ans++;
s += dists[i];
}
return ans;
}
else{
vector<vector<ll>>cost(N, vi(2));
f0r(i, N){
cost[i][0] = min(dist[i][0], dist[i][1]);
cost[i][1] = max(dist[i][0], dist[i][1]);
}
vector<pair<pair<ll,ll>,ll>> l2s;
f0r(i, N){
l2s.pb(mp(mp(max(dist[i][0], dist[i][1]) - min(dist[i][0], dist[i][1]), max(dist[i][0], dist[i][1])), i));
}
sort(l2s.begin(), l2s.end());
vector<ll> dists;
f0r(i, N){
dists.pb(min(dist[i][0], dist[i][1]));
}
sort(dists.begin(), dists.end());
ll ans = 0;
ll s = 0;
f0r(i, N){
if(s + dists[i] <= K){
ans++; s += dists[i];
}
}
ll mx = -4e18;
ll mn = 4e18;
ll twosum = 0;
f0r(i, N){
// cout<<l2s[i].first<<' '<<l2s[i].second<<'\n';
mx = max(mx, l2s[i].second);
mn = min(mn, l2s[i].second);
twosum += max(dist[l2s[i].second][0], dist[l2s[i].second][1]);
ll cur = twosum;
ll curans = (mx - mn + 1) * 2;
if(mn > X){
for(int j = X; j<mn; j++){
cur += dist[j][0];
curans++;
}
}
if(mx < Y){
for(int j = mx + 1; j<=Y; j++){
cur += dist[j][1];
curans++;
}
}
// cout<<twosum<<' '<<cur<<'\n';
if(cur > K)continue;
vi bonk;
for(int j = min((ll)X-1, mn-1); j>=0; j--){
bonk.pb(dist[j][0]);
}
for(int j = max((ll)Y+1, mx+1); j<N; j++){
bonk.pb(dist[j][1]);
}
sort(bonk.begin(), bonk.end());
int ptr = 0;
while(ptr < bonk.size() && bonk[ptr] + cur <= K){
curans++; cur += bonk[ptr]; ptr++;
}
// cout<<i<<' '<<curans<<'\n';
// cout<<'\n';
ans = max(ans, curans);
}
return ans;
}
}
