#include "closing.h"
#include <bits/stdc++.h>
#define MAX 200005
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
int visited[MAX], parent[MAX];
vector<pii> graph[MAX];
ll cost1[MAX], cost2[MAX];
ll dist1[MAX], dist2[MAX];
void init(int node, int par) {
parent[node] = par;
for(auto [v, w] : graph[node]) if(v != par) init(v, node);
}
void dfs(int node, int par, ll dist[]) {
for(auto [v, w] : graph[node]) if(v != par) {
dist[v] = dist[node] + w;
dfs(v, node, dist);
}
}
ll c[MAX];
vector<int> path;
int max_score(int N, int X, int Y, long long K, vector<int> U, vector<int> V, vector<int> W)
{
path.clear();
for(int i = 0; i < N; ++i) graph[i].clear();
for(int i = 0; i < N; ++i) dist1[i] = dist2[i] = visited[i] = c[i] = 0;
for(int i = 0; i < N - 1; ++i) {
graph[U[i]].push_back({V[i], W[i]});
graph[V[i]].push_back({U[i], W[i]});
}
init(0, -1);
dfs(X, -1, dist1);
dfs(Y, -1, dist2);
int node = X;
while(node != -1) visited[node]++, node = parent[node];
node = Y; int flag = 0;
while(node != -1) {
if(visited[node] == 1 && !flag) flag = 1;
else if(flag) visited[node]--;
else visited[node]++;
node = parent[node];
}
node = X;
while(node != -1 && visited[node]) {
path.push_back(node);
node = parent[node];
}
path.pop_back();
vector<int> tmp;
node = Y;
while(node != -1 && visited[node]) {
tmp.push_back(node);
node = parent[node];
}
reverse(tmp.begin(), tmp.end());
for(auto v : tmp) path.push_back(v);
priority_queue<pair<ll, int> > pq;
for(int i = 1; i <= 2 * N; ++i) cost1[i] = (ll)(2e18);
int p = 0, q = path.size() - 1;
for(int i = 1; i <= 2 * N; ++i) {
if(p == path.size() && q == -1) break;
if(p == path.size()) {
cost1[i] = cost1[i - 1] + dist2[path[q]] - c[path[q]];
c[path[q]] = dist2[path[q]]; --q;
}
else if(q == -1) {
cost1[i] = cost1[i - 1] + dist1[path[p]] - c[path[p]];
c[path[p]] = dist1[path[p]]; ++p;
}
else if(dist1[path[p]] - c[path[p]] <= dist2[path[q]] - c[path[q]]) {
cost1[i] = cost1[i - 1] + dist1[path[p]] - c[path[p]];
c[path[p]] = dist1[path[p]]; ++p;
}
else {
cost1[i] = cost1[i - 1] + dist2[path[q]] - c[path[q]];
c[path[q]] = dist2[path[q]]; --q;
}
}
for(int i = 1; i <= 2 * N; ++i) cost2[i] = (ll)(2e18);
for(int i = 0; i < N; ++i) if(!visited[i]) pq.push({-min(dist1[i], dist2[i]), 2 * i + 1});
for(int i = 1; !pq.empty(); ++i) {
ll w = -pq.top().first;
int cur = pq.top().second;
pq.pop();
cost2[i] = min(cost2[i], cost2[i - 1] + w);
if(cur & 1) pq.push({-(max(dist1[cur/2], dist2[cur/2]) - w), cur - 1});
}
int mx = 0;
for(int i = 2 * N, p = 0; i >= 0; --i) {
while(p < 2 * N && cost1[i] + cost2[p + 1] <= K) ++p;
if(cost1[i] + cost2[p] <= K) mx = max(mx, i + p);
}
return mx;
}
