#include "race.h"
#include <bits/stdc++.h>
#define sp <<" "
#define el <<"\n"
#define S second
#define F first
#define pb push_back
#define all(ar) ar.begin(),ar.end()
#define pii pair<ll,ll>
using namespace std;
using ll = long long;
using ld = long double;
const ll mxr = 200005;
const ll big = 2000000999;
ll n,k,path[1000011],mac,ans = big;
vector<vector<pii>> g;
bitset<mxr> ded;
vector<ll> sz(mxr);
void dfs(ll v,ll p){
sz[v] = 1;
for(pii r: g[v]){
if(r.F == p || ded[r.F]) continue;
dfs(r.F,v);
sz[v] += sz[r.F];
}
return;
}
ll fcen(ll v,ll p,ll lim){
for(pii r: g[v]){
if(r.F == p || ded[r.F]) continue;
if(sz[r.F] > lim) return fcen(r.F,v,lim);
}
return v;
}
void fil(ll v,ll p,ll cost,ll dep,unordered_map<ll,ll> &dis){
if(cost > k) return;
ans = min(ans,dep + path[k - cost]);
dis[cost] = dis.count(cost) ? min(dis[cost],dep) : dep;
for(pii r: g[v]){
if(r.F == p || ded[r.F]) continue;
fil(r.F,v,cost + r.S,dep+1,dis);
}
return;
}
void decompose(ll v){
dfs(v,-1);
ll lim = (sz[v]/2);
ll cen = fcen(v,-1,lim);
ded[cen] = 1;
unordered_set<ll> cum;
for(pii r: g[cen]){
if(ded[r.F]) continue;
unordered_map<ll,ll> dis;
fil(r.F,cen,r.S,1,dis);
for(pii x: dis){
cum.insert(x.F);
path[x.F] = min(x.S,path[x.F]);
}
}
ans = min(ans,path[k]);
for(ll i : cum) path[i] = big;
for(pii r: g[cen]){
if(!ded[r.F]) decompose(r.F);
}
}
int best_path(int N, int K, int H[][2], int L[])
{
n = N;
k = K;
g.assign(n,{});
for(ll i = 1; i < n; i++){
ll a = H[i-1][0], b = H[i-1][1], c = L[i-1];
g[a].pb({b,c});
g[b].pb({a,c});
}
for(ll i = 0; i <= 1000010; i++) path[i] = big;
decompose(0);
return ans == big ? -1 : ans;
}
