#include <bits/stdc++.h>
using namespace std;
#define f first
#define s second
#define pb push_back
#define all(x) x.begin(), x.end()
#define sz(x) (long long)(x).size()
#define pii pair<long long, long long>
long long ANS = LLONG_MAX;
void dfs_sze(long long u, long long par, vector<vector<pii>> &adj, vector<long long> &sze, vector<long long> &len, vector<long long> &depth) {
sze[u] = 1;
for (auto v : adj[u]) {
if (v.f != par) {
len[v.f] = len[u] + v.s;
depth[v.f] = depth[u] + 1;
dfs_sze(v.f, u, adj, sze, len, depth);
sze[u] += sze[v.f];
}
}
}
void small_to_large_merging(long long K, long long u, long long par, vector<long long> &sze, vector<long long> &len, vector<long long> &depth, vector<vector<pii>> &adj, vector<multiset<pii>> &sets) {
multiset<pii> smalls1, smalls2;
for (auto x : adj[u]) {
if (x.f != par) {
small_to_large_merging(K, x.f, u, sze, len, depth, adj, sets);
for (auto y : sets[x.f]) {
long long len1 = y.f - len[u];
long long dep = y.s - depth[u];
pii find = {K - len1, -1ll};
auto it = smalls2.lower_bound(find);
if (it != smalls2.end()) {
if (it->f == find.f) {
ANS = min(ANS, dep + it->s);
}
}
}
for (auto y : sets[x.f]) {
smalls1.insert(y);
smalls2.insert({y.f - len[u], y.s - depth[u]});
}
sets[x.f].clear();
}
}
sets[u] = smalls1; // Do not clear after this assignment
sets[u].insert({len[u], depth[u]}); // Include the current node's length and depth
pii find = {K + len[u], -1ll};
auto it = sets[u].lower_bound(find);
if (it != sets[u].end()) {
if (it->f == find.f) {
ANS = min(ANS, it->s - depth[u]);
}
}
}
int best_path(int N, int k, int H[][2], int L[]) {
ANS = LLONG_MAX;
long long n = N, K = k;
vector<vector<pii>> adj(n);
for (long long i = 0; i < n - 1; i++) {
adj[H[i][0]].pb({H[i][1], L[i]});
adj[H[i][1]].pb({H[i][0], L[i]});
}
vector<long long> sze(n, 0);
vector<long long> len(n, 0);
vector<long long> depth(n, 0);
dfs_sze(0, -1, adj, sze, len, depth);
vector<multiset<pii>> sets(n);
small_to_large_merging(K, 0, -1, sze, len, depth, adj, sets);
if (ANS == LLONG_MAX) {
return -1;
}
return ANS;
}
