#include "closing.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define eb emplace_back
#define ALL(a) a.begin(), a.end()
#define ll long long
#define MP make_pair
#define pii pair<int, int>
const ll INF = 1ll << 50;
// const int MXN = 1<<20;
int none(int N, int X, int Y, long long K, std::vector<int> U, std::vector<int> V, std::vector<int> W) {
vector<vector<pii>> adj(N);
for (int i=0; i < N-1; i++) {
adj[V[i]].eb(U[i], W[i]);
adj[U[i]].eb(V[i], W[i]);
}
vector<bool> done(N);
vector<ll> d(N, INF);
d[X] = d[Y] = 0;
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.emplace(0, X);
pq.emplace(0, Y);
int ans = 0;
while (!pq.empty()) {
auto [_, v] = pq.top();
pq.pop();
if (done[v]) continue;
done[v] = true;
if (d[v] <= K) {
ans++;
K -= d[v];
}
for (auto [u, w] : adj[v]) if (d[v]+w < d[u]) {
d[u] = d[v]+w;
pq.push(MP(d[u], u));
}
}
return ans;
}
int max_score(int N, int X, int Y, long long K, std::vector<int> U, std::vector<int> V, std::vector<int> W) {
vector<vector<pii>> adj(N);
for (int i=0; i < N-1; i++) {
adj[V[i]].eb(U[i], W[i]);
adj[U[i]].eb(V[i], W[i]);
}
vector<array<ll, 2>> f(N);
auto dfs = [&](auto self, int v, int p, int c) -> void {
for (auto [u, w] : adj[v]) if (u!=p) {
f[u][c] = f[v][c] + w;
self(self, u, v, c);
}
};
dfs(dfs, X, X, 0);
dfs(dfs, Y, Y, 1);
vector<int> save_by_x(N), save_by_y(N);
iota(ALL(save_by_x), 0);
iota(ALL(save_by_y), 0);
sort(ALL(save_by_x), [&](int v, int u) {
return f[v][0]>f[u][0];
});
sort(ALL(save_by_y), [&](int v, int u) {
return f[v][1]>f[u][1];
});
vector<int> save_c(N, -1);
{
vector<int> stk;
auto DFS = [&](auto self, int v, int p) -> void {
stk.pb(v);
if (v == Y) for (int it : stk) save_c[it] = min(f[it][0], f[it][1]);
for (auto [u, w] : adj[v]) if (u!=p) {
self(self, u, v);
}
stk.pop_back();
};
DFS(DFS, X, X);
}
int ans = none(N, X, Y, K, U, V, W);
auto check = [&](int m, int l) {
vector<int> all;
vector<int> c = save_c;
auto add = [&](auto self, int v, int fa) -> void {
if (c[v] != -1) all.pb(v);
for (auto [u, w] : adj[v]) if (c[u] == -1 && u!=fa) self(self, u, v);
};
vector<int> P;
for (int v=0; v<N; v++) if (c[v] != -1) P.pb(v);
sort(ALL(P), [&](int v, int u) {
return max(f[v][0],f[v][1]) > max(f[u][0],f[u][1]);
});
if (P.size()<l) return -1;
ll k = K;
for (int it : c) if (it != -1) k -= it;
for (int _=0; _<l; _++) {
int v = P.back();
P.pop_back();
if (c[v] != -1) k += c[v];
c[v] = max(f[v][0], f[v][1]);
k -= c[v];
add(add, v, v);
}
sort(ALL(all), [&](int v, int u) {
return max(f[v][0],f[v][1]) > max(f[u][0],f[u][1]);
});
if (all.size()<m) return -1;
for (int _=0; _<m; _++) {
int v = all.back();
all.pop_back();
if (c[v] != -1) k += c[v];
c[v] = max(f[v][0], f[v][1]);
k -= c[v];
}
if (k<0) return -1;
int res = 0;
vector<int> by_x = save_by_x;
vector<int> by_y = save_by_y;
while (!by_x.empty() || !by_y.empty()) {
bool flg = false;
if (!by_x.empty() && !by_y.empty()) {
int v = by_x.back();
int u = by_y.back();
if (f[v][0]<f[u][1]) flg = true;
}
if (by_y.empty() || flg) {
int v = by_x.back();
by_x.pop_back();
if (f[v][1]<=f[v][0] && c[v] < f[v][0]) continue;
if (c[v] != -1 || f[v][0]<=k) {
res++;
if (c[v] == -1) k -= f[v][0];
}
}
else {
int v = by_y.back();
by_y.pop_back();
if (f[v][0]<=f[v][1] && c[v] < f[v][1]) continue;
if (c[v] != -1 || f[v][1]<=k) {
res++;
if (c[v] == -1) k -= f[v][1];
}
}
}
return res;
};
// for (int k=MXN; 1<=k; k>>=1) if (m+k <= N && check(m+k) != -1) m += k;
// return max(ans, check(m));
for (int m=0; m <= N; m++) for (int l=1; l <= N; l++) ans = max(ans, check(m, l));
return ans;
}
