#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 tmp[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 mx = 0; ll sum = 0;
priority_queue<pair<ll, int> > pq;
pq.push({0, X}); pq.push({0, Y});
while(!pq.empty()) {
ll d = -pq.top().first;
int node = pq.top().second;
pq.pop();
if(sum + d > K) break;
++mx; sum += d; visited[node] = 1;
for(auto [v, w] : graph[node]) {
if(visited[v]) continue;
pq.push({-(d + w), v});
}
}
if(dist1[Y] > 2 * K) return mx;
int node = X;
for(int i = 0; i < N; ++i) visited[i] = 0;
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();
node = Y;
vector<int> path2;
while(node != -1 && visited[node]) {
path2.push_back(node);
node = parent[node];
}
reverse(path2.begin(), path2.end());
for(auto v : path2) path.push_back(v);
int p = 0, q = path.size() - 1, r; cost1[0] = 0;
for(int i = 1; i <= 2 * N; ++i) cost1[i] = (ll)(2e18);
for(int i = 1; i <= 2 * N; ++i) {
int u = p == (int)path.size() ? -1 : path[p];
int v = q == -1 ? -1 : path[q];
if(u == -1 && v == -1) break;
if(u == v) r = i;
if(u == -1) {
cost1[i] = cost1[i - 1] + dist2[v] - c[v];
c[v] = dist2[v]; --q;
}
else if(v == -1) {
cost1[i] = cost1[i - 1] + dist1[u] - c[u];
c[u] = dist1[u]; ++p;
}
else if(dist1[u] - c[u] <= dist2[v] - c[v]) {
cost1[i] = cost1[i - 1] + dist1[u] - c[u];
c[u] = dist1[u]; ++p;
}
else {
cost1[i] = cost1[i - 1] + dist2[v] - c[v];
c[v] = dist2[v]; --q;
}
}
for(int i = 0; i < r; ++i) cost1[i] = (ll)(2e18);
for(int i = 1; i <= 2 * N; ++i) cost2[i] = (ll)(2e18);
for(int i = 0; i < N; ++i) {
if(visited[i]) continue;
for(int j = 0; j <= 2 * N; ++j) tmp[j] = cost2[j];
for(int j = 1; j <= 2 * N; ++j) {
tmp[j] = min(tmp[j], cost2[j - 1] + min(dist1[i], dist2[i]));
if(j >= 2) tmp[j] = min(tmp[j], cost2[j - 2] + max(dist1[i], dist2[i]));
}
for(int j = 0; j <= 2 * N; ++j) cost2[j] = tmp[j];
}
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;
}
