#include "closing.h"
#include <bits/stdc++.h>
#define ll long long
#define endl "\n"
using namespace std;
const ll N = 2e5 + 5;
vector<pair<ll, ll>> g[N];
void dfs(ll v, ll par, vector<ll> &depth)
{
for (auto [to, w] : g[v])
if (to != par)
{
depth[to] = depth[v] + w;
dfs(to, v, depth);
}
}
vector<ll> getpath(ll x, ll y, vector<ll> &d)
{
vector<ll> path;
while (x != y and path.size() <= d.size())
{
path.push_back(x);
for (auto [i, w] : g[x]) if (d[i] < d[x])
{
x = i;
break;
}
}
path.push_back(y);
return path;
}
ll n;
int max_score(int N, int X, int Y, long long k,
std::vector<int> U, std::vector<int> V, std::vector<int> W)
{
n = N;
for (ll i = 0; i < n; i++) g[i].clear();
for (ll i = 0; i + 1 < n; i++) g[U[i]].push_back(make_pair(V[i], W[i])), g[V[i]].push_back(make_pair(U[i], W[i]));
vector<ll> a(n), b(n);
dfs(X, -1, a);
dfs(Y, -1, b);
ll ans = 0, ptr = n - 1, sum = 0;
vector<ll> path = getpath(X, Y, b);
a.insert(a.begin(), 0);
b.insert(b.begin(), 0);
bool onpath[n + 1];
for (ll i = 1; i <= n; i++) onpath[i] = 0;
for (ll i : path) i++, onpath[i] = 1, k -= min(a[i], b[i]);
ll dp[n + 1][2 * n + 1];
for (ll i = 0; i <= n; i++)
for (ll j = 0; j <= 2 * n; j++) dp[i][j] = 1e18 + 1;
dp[0][0] = 0;
for (ll i = 1; i <= n; i++)
{
for (ll j = 0; j <= 2 * n; j++)
dp[i][j] = min(dp[i][j], dp[i - 1][j]);
for (ll j = 0; j <= 2 * n; j++)
{
if (j + 1 <= 2 * n)
dp[i][j + 1] = min(dp[i][j + 1], dp[i - 1][j] + (onpath[i] ? 0 : min(a[i], b[i])));
if (j + 2 <= 2 * n)
dp[i][j + 2] = min(dp[i][j + 2], dp[i - 1][j] + (onpath[i] ? abs(a[i] - b[i]) : max(a[i], b[i])));
}
}
for (ll j = 0; j <= 2 * n; j++) if (dp[n][j] <= k) ans = j;
a.erase(a.begin());
b.erase(b.begin());
for (ll i = 0; i < n; i++) sum += b[i];
for (ll i : path) k += min(a[i], b[i]);
sort(a.begin(), a.end());
sort(b.begin(), b.end());
if (sum <= k) ans = max(ans, n);
for (ll i = 0; i < n; i++)
{
sum += a[i];
while (ptr >= 0 and sum > k) sum -= b[ptr--];
if (sum <= k) ans = max(ans, ptr + 1 + i + 1);
}
return ans;
}
