// #include "closing.h"
#include <bits/stdc++.h>
using namespace std;
// #pragma GCC optimize ("Ofast")
// #pragma GCC target ("avx2")
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
#define el << '\n'
#define nl cout << '\n'
#define spc << ' '
#define forn(i,n) for (int i=0; i<n; i++)
#define forl(i,s,e) for (int i=s; i<e; i++)
#define pb push_back
#define fi first
#define se second
#define rsz resize
#define sz(x) ((int) x.size())
#define all(x) x.begin(), x.end()

int max_score(int N, int X, int Y, ll K, vector<int> U, vector<int> V, vector<int> W) {
	vector<pll> dis(N);
	vector<vector<pll>> adj(N);
	struct st {
		int cn, pn; ll d; bool p;
	};
	forn(i,N-1) {
		adj[U[i]].pb({V[i], W[i]});
		adj[V[i]].pb({U[i], W[i]});
	}
	vector<st> stk;
	stk.pb({X, -1, 0, 0});
	while (sz(stk)) {
		st a = stk.back();
		stk.pop_back();
		if (a.p) dis[a.cn].se = a.d;
		else dis[a.cn].fi = a.d;
		for (pii i : adj[a.cn]) if (i.fi != a.pn) stk.pb({i.fi, a.cn, a.d+i.se, a.p});
	}
	stk.pb({Y, -1, 0, 1});
	while (sz(stk)) {
		st a = stk.back();
		stk.pop_back();
		if (a.p) dis[a.cn].se = a.d;
		else dis[a.cn].fi = a.d;
		for (pii i : adj[a.cn]) if (i.fi != a.pn) stk.pb({i.fi, a.cn, a.d+i.se, a.p});
	}
	forn(i,N) if (dis[i].fi < dis[i].se) swap(dis[i].fi, dis[i].se);
	sort(all(dis));
	vector<bool> u(N);
	forn(i,N) u[i] = false;
	priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
	priority_queue<pair<ll, int>> rpq;
	// forn(i,N) cout << dis[i].fi spc << dis[i].se el;
	// nl;
	forn(i,N) pq.push({dis[i].se, i});
	int tot = 0;
	while (1) {
		ll temp = K - pq.top().fi;
		if (temp < 0) break;
		u[pq.top().se] = 1;
		rpq.push(pq.top());
		pq.pop();
		K = temp;
		tot++;
	}
	// cout << K spc << tot el;
	int ans = tot;
	forn(i,N) {
		if (u[i]) {
			K += dis[i].se;
			tot--;
		}
		K -= dis[i].fi;
		tot += 2;
		bool temp = false;
		while (K<0) {
			if (!sz(rpq)) {
				temp = true;
				break;
			}
			auto cn = rpq.top();
			rpq.pop();
			if (cn.se <= i) continue;
			tot--;
			K += cn.fi;
		}
		if (temp) break;
		ans = max(ans, tot);
		// cout << K spc << tot el;
	}
	return ans;	
}