#include "race.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
struct thing {
int dist, d, u;
bool operator < (const thing &b) const {
if (dist!=b.dist) return dist < b.dist;
if (d!=b.d) return d < b.d;
return u < b.u;
}
};
struct node {
pair<int,int> val;
int lpt, rpt;
};
const int maxn = 2e5 + 5, maxN = 8e5 + 5, INF = 1e18;
int n, k;
vector<pair<int,int>> adj[maxn];
int sz[maxn], dist[maxn], d[maxn];
bool cmp(pair<int,int> x, pair<int,int> y) {
return sz[x.first] > sz[y.first];
}
void dfs0(int u) {
sz[u] = 1;
for (auto [v, w]:adj[u]) {
adj[v].erase(find(adj[v].begin(), adj[v].end(), make_pair(u, w)));
dist[v] = dist[u] + w, d[v] = d[u] + 1;
dfs0(v);
sz[u] += sz[v];
}
sort(adj[u].begin(), adj[u].end(), cmp);
}
int newid[maxn], oldid[maxn], lim[maxn], cnt = -1;
void dfs1(int u) {
cnt++;
newid[u] = cnt, oldid[cnt] = u;
for (auto [v, w]:adj[u]) dfs1(v);
lim[u] = cnt;
}
vector<node> seg[maxN];
void build(int id, int l, int r) {
seg[id] = {{{-INF, -INF}, 0, 0}};
if (l==r) return;
int mid = (l+r)/2;
build(id*2, l, mid); build(id*2+1, mid+1, r);
}
void update(int id, int l, int r, int target, pair<int,int> val) {
if (r<target || target<l) return;
if (l==r) {
seg[id].push_back({val, 0, 0});
return;
}
int mid = (l+r)/2;
update(id*2, l, mid, target, val); update(id*2+1, mid+1, r, target, val);
pair<int,int> cur = max(seg[id*2].back().val, seg[id*2+1].back().val);
seg[id].push_back({cur, (int)seg[id*2].size()-1, (int)seg[id*2+1].size()-1});
}
pair<int,int> qry(int id, int pt, int l, int r, int findl, int findr) {
if (r<findl || findr<l) return {-INF, -INF};
if (findl<=l && r<=findr) return seg[id][pt].val;
int mid = (l+r)/2;
pair<int,int> lhs = qry(id*2, seg[id][pt].lpt, l, mid, findl, findr);
pair<int,int> rhs = qry(id*2+1, seg[id][pt].rpt, mid+1, r, findl, findr);
return max(lhs, rhs);
}
int ans = INF, curD;
vector<thing> vec = {{-INF, -INF, -INF}};
void QRY(int l, int r, int val) {
if (val<0) return;
thing cur = {val, INF, INF};
int pos = upper_bound(vec.begin(), vec.end(), cur) - vec.begin() - 1;
// cout << l << " " << r << " " << val << " " << pos << endl;
pair<int,int> temp = qry(1, pos, 0, n-1, l, r);
// cout << temp.first << " " << temp.second << endl;
if (temp.first!=val) return;
ans = min(-temp.second + curD, ans);
}
int32_t best_path(int32_t N, int32_t K, int32_t H[][2], int32_t L[]) {
n = N, k = K;
for (int i=0;i<n-1;i++) {
auto [u, v] = H[i];
adj[u].push_back({v, L[i]});
adj[v].push_back({u, L[i]});
}
dist[0] = 0, d[0] = 0;
dfs0(0); dfs1(0);
// for (int i=0;i<n;i++) cout << newid[i] << " "; cout << endl;
for (int i=0;i<n;i++) vec.push_back({dist[i], -d[i], newid[i]});
sort(vec.begin(), vec.end());
build(1, 0, n-1);
for (int i=1;i<=n;i++) {
update(1, 0, n-1, vec[i].u, {vec[i].dist, vec[i].d});
// cout << i << " " << vec[i].u << " " << vec[i].dist << " " << vec[i].d << endl;
}
for (int u=0;u<n;u++) {
curD = -d[u];
// if (u==6) cout << "TEST" << endl;
QRY(newid[u]+1, lim[u], k + dist[u]);
// if (u==6) cout << k+dist[u] << endl;
for (int i=1;i<adj[u].size();i++) {
int v = adj[u][i].first;
for (int j=newid[v];j<=lim[v];j++) {
curD = -2*d[u] + d[oldid[j]];
QRY(newid[u]+1, newid[v]-1, k + 2*dist[u] - dist[oldid[j]]);
}
}
}
if (ans==INF) return -1;
return ans;
}
