#include "closing.h"
#include <bits/stdc++.h>
using namespace std;
vector <pair <int, int>> ke[200001];
long long d[200001][2],cur;
int p[200001],ch[200001],vis[200001],inset[200001];
set <pair <long long, int>> s,s2;
void dfs(int u, int i, int par=-1){
for (auto [v,w]:ke[u])
if (v!=par){
d[v][i]=d[u][i]+w;
p[v]=u;
dfs(v,i,u);
}
}
void dfs2(int u, int par){
for (auto [v,w]:ke[u]){
if (!ch[v]&&v!=par){
if (!vis[v]&&min(d[v][0],d[v][1])*2>max(d[v][0],d[v][1])){
s2.insert({max(d[v][0],d[v][1]),v});
inset[v]=1;
}
dfs2(v,u);
}
}
}
int max_score(int N, int X, int Y, long long K, vector<int> U, vector<int> V, vector<int> W){
for (int i=0;i<N-1;i++){
ke[U[i]].push_back({V[i],W[i]});
ke[V[i]].push_back({U[i],W[i]});
}
memset(ch,0,sizeof(ch));
memset(inset,0,sizeof(inset));
memset(vis,0,sizeof(vis));
d[X][0]=d[Y][1]=0;
dfs(X,0);
dfs(Y,1);
for (;X!=Y;X=p[X])
ch[X]=1;
ch[Y]=1;
int res=0,cnt=0;
for (int i=0;i<N;i++)
s.insert({min(d[i][0],d[i][1]),i});
cur=0;
while (!s.empty()&&cur+(*s.begin()).first<=K){
cur+=(*s.begin()).first;
res++;
s.erase(s.begin());
}
s.clear();
cur=0;
for (int i=0;i<N;i++){
if (ch[i]){
s.insert({abs(d[i][0]-d[i][1]),i});
cur+=min(d[i][0],d[i][1]);
cnt++;
}
else{
s.insert({min(d[i][0],d[i][1]),i});
if (min(d[i][0],d[i][1])*2<=max(d[i][0],d[i][1]))
s.insert({abs(d[i][0]-d[i][1]),i});
}
}
while (!s.empty()){
int x=0,i=0,y=0;
auto [c,u]=*s.begin();
s.erase(s.begin());
if (s2.empty())
x=c,i=u,y=1;
else{
auto [c2,u2]=*s2.begin();
s2.erase(s2.begin());
if (s.empty()){
s.insert({c,u});
x=c2;
i=u2;
y=2;
}
else{
if (u!=u2&&c+(*s.begin()).first<c2){
s2.insert({c2,u2});
x=c;
i=u;
y=1;
}
else{
s.insert({c,u});
x=c2;
i=u2;
y=2;
}
}
}
if (cur+x>K)
break;
cur+=x;
cnt+=y;
if (y==1&&!vis[i]){
if (ch[i])
dfs2(i,i);
else{
s.insert({abs(d[i][0]-d[i][1]),i});
if (inset[i])
s2.erase(s2.find({max(d[i][0],d[i][1]),i}));
}
}
if (y==2&&!vis[i])
s.erase(s.find({min(d[i][0],d[i][1]),i}));
vis[i]=1;
}
while (!s.empty()&&cur+(*s.begin()).first<=K){
cur+=(*s.begin()).first;
cnt++;
s.erase(s.begin());
}
while (!s2.empty()&&cur+(*s2.begin()).first<=K){
cur+=(*s2.begin()).first;
cnt+=2;
s2.erase(s2.begin());
}
s.clear();
s2.clear();
for (int i=0;i<N;i++)
ke[i].clear();
return max(res,(cur>K?0:cnt));
}
