#include "race.h"
#include <bits/stdc++.h>
using namespace std;
int best_path(int N, int K, int H[][2], int L[])
{
int n = N;
int k = K;
vector<vector<pair<int, int>>> g(n);
for (int i = 0; i < n - 1; ++i) {
int x = H[i][0];
int y = H[i][1];
int z = L[i];
g[x].emplace_back(y, z);
g[y].emplace_back(x, z);
}
vector<bool> removed(n, false);
auto GetCenter = [&](int r) {
vector<int> sz(n);
vector<int> pv(n);
auto DFS = [&](auto&& self, int v) -> void {
sz[v] = 1;
for (auto [u, _] : g[v]) {
if (u != pv[v] && !removed[u]) {
pv[u] = v;
self(self, u);
sz[v] += sz[u];
}
}
};
pv[r] = -1;
DFS(DFS, r);
while (true) {
int nr = -1;
for (auto [u, _] : g[r]) {
if (u != pv[r] && !removed[u] && sz[u] * 2 > sz[r]) {
nr = u;
break;
}
}
if (nr == -1) {
return r;
}
r = nr;
}
};
vector<int> dp(k + 1, n);
auto Find = [&](auto&& self, int v, int pv, int dist, int edges) -> void {
for (auto [u, w] : g[v]) {
if (u != pv && dist + w <= k && !removed[u]) {
dp[dist + w] = min(dp[dist + w], edges + 1);
dp[k] = min(dp[k], dp[k - w] + 1);
self(self, u, v, dist + w, edges + 1);
}
}
};
auto Solve = [&](auto&& self, int v) -> void {
int c = GetCenter(v);
removed[c] = true;
Find(Find, c, -1, 0, 0);
for (auto [u, _] : g[c]) {
if (!removed[u]) {
self(self, u);
}
}
};
Solve(Solve, 0);
return (dp[k] == n ? -1 : dp[k]);
}
