#include "closing.h"
#include <vector>
#include <bits/stdc++.h>
using namespace std;
void dfs(int st, vector<array<int,2>>g[], int p, long long dist[], long long d){
dist[st]=d;
for(array<int,2>e:g[st]){
if(e[0]==p)
continue;
dfs(e[0],g,st,dist,d+e[1]);
}
}
vector<int>xypath;
void dfsxy(int st, vector<array<int,2>>g[], int p, vector<int>&path, int y){
path.push_back(st);
if(st==y){
xypath.clear();
for(int i : path){
xypath.push_back(i);
}
}
for(array<int,2>e : g[st]){
if(e[0]==p)
continue;
dfsxy(e[0],g,st,path,y);
}
path.pop_back();
}
int max_score(int n, int x, int y, long long k, vector<int> u, vector<int> v, vector<int> w) {
vector<array<int,2>>g[n];
int m = u.size();
for(int i = 0;i<m;i++){
g[u[i]].push_back({v[i],w[i]});
g[v[i]].push_back({u[i],w[i]});
}
long long distx[n], disty[n];
dfs(x,g,-1,distx,0);
dfs(y,g,-1,disty,0);
long long cost1[n],cost2[n];
for(int i = 0;i<n;i++){
cost1[i]=min(distx[i],disty[i]);
cost2[i]=max(distx[i],disty[i])-cost1[i];
}
vector<int>pt;
dfsxy(x,g,-1,pt,y);
//case 1:
int ans1 = 0;
//only till level 1.
priority_queue<long long,vector<long long>,greater<long long>>pq;
for(int i = 0;i<n;i++){
pq.push(cost1[i]);
}
long long curk = 0;
while(curk<=k&&pq.size()){
long long a = pq.top();
pq.pop();
if(curk+a>k)
break;
ans1++;
curk+=a;
}
//case 2:
bool man[n];
fill(man,man+n,0);
for(int i : xypath){
man[i]=1;
}
long long dp[n][n*2+1];
bool temp = 0;
for(int i = 0;i<n;i++){
fill(dp[i],dp[i]+n*2+1,2e18);
dp[i][0]=0;
if(man[i]||temp){
dp[i][0]=2e18;
temp = 1;
}
}
dp[0][1]=cost1[0];
dp[0][2]=cost1[0]+cost2[0];
for(int i = 1;i<n;i++){
for(int j = 1;j<=2*n;j++){
if(man[i]){
//must take atleast one.
dp[i][j]=dp[i-1][j-1]+cost1[i];
}
else{
dp[i][j]=min({dp[i-1][j],dp[i-1][j-1]+cost1[i]});
}
if(j>1){
dp[i][j]=min(dp[i][j],dp[i-1][j-2]+cost1[i]+cost2[i]);
}
dp[i][j]=min((long long)2e18,dp[i][j]);
}
}
int ans2 = 0;
for(int j = 0;j<=2*n;j++){
if(dp[n-1][j]<=k){
ans2=max(ans2,j);
}
}
return max(ans1,ans2);
}
