#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
refs:
https://codeforces.com/blog/entry/121499
*/
const int MOD = 1e9 + 7;
const int N = 2e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "closing.h"
vector<pll> adj[N];
ll dis[N][2];
void dfs1(ll u, ll p, ll t){
for(auto [v,w] : adj[u]){
if(v == p) conts;
dis[v][t] = dis[u][t]+w;
dfs1(v,u,t);
}
}
vector<bool> on_path(N);
vector<ll> curr_path;
void dfs2(ll u, ll p, ll des){
curr_path.pb(u);
if(u == des){
trav(v,curr_path){
on_path[v] = 1;
}
}
for(auto [v,w] : adj[u]){
if(v == p) conts;
dfs2(v,u,des);
}
curr_path.pop_back();
}
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,n){
adj[i].clear();
on_path[i] = 0;
}
rep(i,n-1){
ll u = U[i], v = V[i], w = W[i];
adj[u].pb({v,w}), adj[v].pb({u,w});
}
dis[X][0] = dis[Y][1] = 0;
dfs1(X,-1,0);
dfs1(Y,-1,1);
dfs2(X,-1,Y);
vector<ll> a(n), b(n);
rep(i,n){
ll dx = dis[i][0], dy = dis[i][1];
a[i] = min(dx,dy);
b[i] = max(dx,dy)-a[i];
}
ll ans = 0;
// only 1s
{
vector<ll> vals;
rep(i,n) vals.pb(a[i]);
sort(all(vals));
ll sum = 0;
ll guys = 0;
rep(i,n){
sum += vals[i];
if(sum > K) break;
guys++;
}
amax(ans,guys);
}
// 1s and 2s
// all guys on path from X to Y must be at least 1
vector<ll> dp1(2*n+5,inf2), dp2(2*n+5);
dp1[0] = 0;
rep(i,n){
fill(all(dp2),inf2);
rep(j,2*n+1){
// 0
if(!on_path[i]){
amin(dp2[j],dp1[j]);
}
// 1
amin(dp2[j+1],dp1[j]+a[i]);
// 2
amin(dp2[j+2],dp1[j]+a[i]+b[i]);
}
dp1 = dp2;
}
rep(j,2*n+1){
if(dp1[j] <= K){
amax(ans,(ll)j);
}
}
return ans;
}
