#include <bits/stdc++.h>
#include "race.h"
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")
#define fio ios_base::sync_with_stdio(0);cin.tie(0);
#define ll long long
#define ld long double
#define en exit(0);
#define pb push_back
#define fi first
#define se second
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int N = 2e5 + 5;
const int K = 1e6 + 5;
const int INF = 1e9 + 5;
vector<pair<int,int> > g[N];
vector<int> vert, vals;
int best[K], sub[N], len[N];
ll dist[N];
int k, res = INF;
bool ban[N];
int get_centroid(int u, int p, int sz)
{
sub[u] = 1;
int mx = -1;
for(auto [v, w] : g[u])
{
if(!ban[v] && v != p)
{
int t = get_centroid(v, u, sz);
if(t != -1)
return t;
sub[u] += sub[v];
mx = max(mx, sub[v]);
}
}
mx = max(mx, sz - sub[u]);
if(mx <= sz / 2)
return u;
return -1;
}
void dfs(int u, int p)
{
for(auto [v, w] : g[u])
{
if(!ban[v] && v != p)
{
len[v] = len[u] + 1;
dist[v] = dist[u] + w;
dfs(v, u);
}
}
vert.pb(u);
}
void go(int u)
{
int sz = sub[u];
u = get_centroid(u, u, sz);
get_centroid(u, u, sz);
ban[u] = 1;
for(auto [v, w] : g[u])
{
if(!ban[v])
{
vert.clear();
dist[v] = w;
len[v] = 1;
dfs(v, v);
for(auto x : vert)
{
ll l = len[x], d = dist[x];
if(k - d >= 0)
res = min(1ll * res, l + best[k - d]);
}
for(auto x : vert)
{
ll l = len[x], d = dist[x];
if(d <= k)
{
best[d] = min(1ll * best[d], l);
vals.pb(d);
}
}
}
}
for(auto x : vals)
best[x] = INF;
best[0] = 0;
vals.clear();
for(auto [v, w] : g[u])
if(!ban[v])
go(v);
}
int best_path(int N, int K, int H[][2], int L[])
{
k = K;
for(int i = 0;i <= k;i++)
best[i] = INF;
best[0] = 0;
for(int i = 0;i < N - 1;i++)
{
int u = H[i][0], v = H[i][1], w = L[i];
g[u].pb({v, w});
g[v].pb({u, w});
}
sub[0] = N;
go(0);
return (res == INF ? -1 : res);
}
