#include <bits/stdc++.h>
using namespace std;
#define ll __int128
const int mod = 1e9+7;
#define forn(i,n) for(int i=0; i<n; i++)
#define readv(a,n) vector<int>a(n);forn(i,n)cin>>a[i];
#define readvv(a,n,m) vector<vector<int>> a(n,vector<int>(m));forn(i,n)forn(j,m)cin>>a[i][j];
#define all(a) a.begin(), a.end()
#define _max(x,y) x = max(x,y)
#define _min(x,y) x = min(x,y)
// #define f first
// #define s second
const int MAXN = 2e5+5;
const int MAXM = 1e6+5;
vector<pair<int,int>> adj[MAXN];
int sbt[MAXN];
vector<int> ch[MAXN];
vector<pair<int,int>> inf[MAXN];
int pn[MAXM];
int rem[MAXN];
int mk[MAXN];
int par[MAXN];
void dfs(int i, int p) {
sbt[i] = 1;
for (auto [c, w]: adj[i]) {
if (c==p || rem[c]) continue;
dfs(c, i);
sbt[i] += sbt[c];
}
}
int ctd(int i, int p, int sz) {
for (auto [c,w] : adj[i]) {
if (c==p || rem[c]) continue;
if (2*sbt[c] > sz) return ctd(c, i, sz);
}
return i;
}
void calc(int i, int p, int dsw, int dse, int tp) {
if (dsw >= MAXM) dsw = MAXM;
if (i!=p) inf[tp]. push_back({dsw, dse});
for (auto [c,w]: adj[i]) {
if (c==p || rem[c]) continue;
calc(c, i, dsw+w, dse+1, tp);
}
}
int build(int i) {
dfs(i, 0);
int x = ctd(i, i, sbt[i]);
rem[x] = 1;
for (auto [c,w] : adj[x]) {
if (rem[c]) continue;
ch[x].push_back(build(c));
par[ch[x].back()] = x;
}
return x;
}
int k;
int ans = MAXM;
void solve(int i) {
rem[i] = 1;
for (auto [c,w]:adj[i]) {
if (rem[c]) continue;
int tp = c;
while (par[tp] != i) tp = par[tp];
calc(c, i, w, 1, tp);
}
for (int c: ch[i]) {
for (auto [dsw, dse]: inf[c]) {
if (dsw >= MAXM) continue;
pn[dsw] = MAXM;
if (dsw <= k) pn[k-dsw] = MAXM;
}
}
pn[0] = 0;
for (int c: ch[i]) {
for (auto [dsw, dse]: inf[c]) {
if (dsw > k) continue;
ans = min(ans, pn[k-dsw] + dse);
}
for (auto[dsw, dse]: inf[c]) {
if (dsw > k) continue;
pn[dsw] = min(pn[dsw], dse);
}
}
for (int c: ch[i]) solve(c);
}
int best_path(int N, int K, int H[][2], int L[])
{
k = K;
for (int i=0; i<N-1; i++) {
H[i][0] ++; H[i][1] ++;
adj[H[i][0]].push_back({H[i][1], L[i]});
adj[H[i][1]].push_back({H[i][0], L[i]});
}
int centr = build(1);
for (int i=0; i<N+3; i++) rem[i] = 0;
solve(centr);
if (ans < MAXM)return ans;
return -1;
}
