/*************************************
* author: marvinthang *
* created: 18.01.2024 09:24:21 *
*************************************/
#include "closing.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i-- > 0; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
template <class A, class B> bool minimize(A &a, B b) { return a > b ? a = b, true : false; }
template <class A, class B> bool maximize(A &a, B b) { return a < b ? a = b, true : false; }
// end of template
int max_score(int N, int X, int Y, long long K, vector <int> U, vector <int> V, vector <int> W) {
vector <long long> dx(N), dy(N);
vector <int> par(N);
vector <vector <pair <int, int>>> adj(N);
REP(i, N - 1) {
adj[U[i]].emplace_back(W[i], V[i]);
adj[V[i]].emplace_back(W[i], U[i]);
}
function<void(int, vector <long long> &)> dfs = [&] (int u, vector <long long> &dist) {
for (auto [w, v]: adj[u]) if (v != par[u]) {
par[v] = u;
dist[v] = dist[u] + w;
dfs(v, dist);
}
};
par[X] = -1; dfs(X, dx);
par[Y] = -1; dfs(Y, dy);
vector <int> values(ALL(dx));
values.insert(values.end(), ALL(dy));
sort(ALL(values));
int res = 0;
long long cur = K;
for (long long c: values) {
cur -= c;
if (cur < 0) break;
++res;
}
if (N > 3000) return res;
vector <bool> on_path(N);
for (; X != Y; X = par[X]) on_path[X] = true;
on_path[X] = true;
vector dp(N + 1, vector(N + N + 1, K + 1));
dp[0][0] = 0;
REP(i, N) REP(j, i + i + 1) if (dp[i][j] <= K) {
minimize(dp[i + 1][j + 1], dp[i][j] + min(dx[i], dy[i]));
minimize(dp[i + 1][j + 2], dp[i][j] + max(dx[i], dy[i]));
if (!on_path[i]) minimize(dp[i + 1][j], dp[i][j]);
}
REPD(j, N + N + 1) if (dp[N][j] <= K) {
maximize(res, j);
break;
}
return res;
}
