#include "bits/stdc++.h"
using namespace std;
#ifdef ONLINE_JUDGE
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> OST;
#endif
#define int long long
#define double long double
#define mp make_pair
#define fi first
#define se second
#define pb push_back
#define all(a) a.begin(),a.end()
const int MOD = 1000000007;
const int MOD2 = 998244353;
const int BIG = 1197423052705914509LL;
mt19937 rng((int) std::chrono::steady_clock::now().time_since_epoch().count());
const int MAXN = 2e5 + 10;
const int NO_OPERATION = 69420420420LL;
const int is_query = -BIG;
struct line {
int m, b;
mutable function<const line*()> succ;
bool operator<(const line& rhs) const {
if (rhs.b != is_query) return m < rhs.m;
const line* s = succ();
if (!s) return 0;
int x = rhs.m;
return b - s->b < (s->m - m) * x;
}
};
struct dynamic_hull : public multiset<line> {
const int inf = BIG;
bool bad(iterator y) {
auto z = next(y);
if (y == begin()) {
if (z == end()) return 0;
return y->m == z->m && y->b <= z->b;
}
auto x = prev(y);
if (z == end()) return y->m == x->m && y->b <= x->b;
int v1 = (x->b - y->b);
if (y->m == x->m) v1 = x->b > y->b ? inf : -inf;
else v1 /= (y->m - x->m);
int v2 = (y->b - z->b);
if (z->m == y->m) v2 = y->b > z->b ? inf : -inf;
else v2 /= (z->m - y->m);
return v1 >= v2;
}
void insert_line(int m, int b) {
auto y = insert({m,b});
y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
if (bad(y)) { erase(y); return; }
while (next(y) != end() && bad(next(y))) erase(next(y));
while (y != begin() && bad(prev(y))) erase(prev(y));
}
int eval(int x) {
auto l = *lower_bound((line) { x, is_query });
return l.m * x + l.b;
}
};
struct auxiliary_tree{
int n;
vector<int>ori[MAXN];
vector<int>storelatest;
int tin[MAXN], tout[MAXN], dep[MAXN], cor[MAXN];
bool imp[MAXN];
int run=0;
vector<int>euler;
vector<vector<pair<int,int> > >lca_table;
int lef[MAXN], rig[MAXN];
void dfs(int node,int prev,int de){
dep[node]=de;
tin[node]=++run;
cor[tin[node]]=node;
euler.pb(node);
for(int i=0;i<ori[node].size();i++){
if(ori[node][i]!=prev){
dfs(ori[node][i],node,de+1);
euler.pb(node);
}
}
tout[node]=++run;
}
void find_all_lcas(){
int k=log2(2*n-1);
lca_table.resize(k+1);
for(int i=0;i<k+1;i++){
lca_table[i].resize(2*n-1);
}
for(int i=0;i<2*n-1;i++){
lca_table[0][i]=mp(dep[euler[i]],euler[i]);
}
for(int i=1;i<=k;i++){
for(int j=0;j<2*n-1;j++){
if(j+(1<<(i-1))>=2*n-1)continue;
if(lca_table[i-1][j].fi<lca_table[i-1][j+(1<<(i-1))].fi){
lca_table[i][j].fi=lca_table[i-1][j].fi;
lca_table[i][j].se=lca_table[i-1][j].se;
}
else{
lca_table[i][j].fi=lca_table[i-1][j+(1<<(i-1))].fi;
lca_table[i][j].se=lca_table[i-1][j+(1<<(i-1))].se;
}
}
}
for(int i=0;i<MAXN;i++) lef[i]=-1;
for(int i=0;i<2*n-1;i++){
if(lef[euler[i]]==-1){
lef[euler[i]]=i;
}
rig[euler[i]]=i;
}
}
bool isParent(int u,int v){
return tin[u]<tin[v] && tout[v]<tout[u];
}
public:
vector<int>adj[MAXN];
int root;
int lcadep(int x,int y){
if(lef[x]>rig[y]){
swap(x,y);
}
int k=log2(rig[y]-lef[x]+1);
return min(lca_table[k][lef[x]].fi,lca_table[k][rig[y]-(1<<k)+1].fi);
}
int lcaidx(int x,int y){
if(lef[x]>rig[y]){
swap(x,y);
}
int k=log2(rig[y]-lef[x]+1);
if(lca_table[k][lef[x]].fi<lca_table[k][rig[y]-(1<<k)+1].fi){
return lca_table[k][lef[x]].se;
}
else{
return lca_table[k][rig[y]-(1<<k)+1].se;
}
}
void base(int x,int rt,vector<int>y[]){
n=x;
for(int i=1;i<=n;i++){
ori[i]=y[i];
}
dfs(rt,-1,0);
find_all_lcas();
}
void build(vector<int>g){
for(int i=0;i<g.size();i++){
g[i]=tin[g[i]];
}
sort(all(g));
for(int i=0;i<g.size();i++){
g[i]=cor[g[i]];
}
int k=g.size();
for(int i=0;i<k-1;i++){
g.pb(lcaidx(g[i],g[i+1]));
}
for(int i=0;i<g.size();i++){
g[i]=tin[g[i]];
}
sort(all(g));
for(int i=0;i<g.size();i++){
g[i]=cor[g[i]];
}
g.erase(unique(all(g)),g.end());
for(int i=0;i<g.size();i++){
imp[g[i]]=1;
storelatest.pb(g[i]);
}
stack<int>vert;
vert.push(g[0]);
for(int i=1;i<g.size();i++){
int u=g[i];
while(vert.size()>1 && isParent(vert.top(),u)==0){
int sto=vert.top();
vert.pop();
adj[vert.top()].pb(sto);
}
vert.push(u);
}
while(vert.size()>1){
int sto=vert.top();
vert.pop();
adj[vert.top()].pb(sto);
}
root=vert.top();
}
void clear(){
for(int i=0;i<storelatest.size();i++){
imp[storelatest[i]]=0;
adj[storelatest[i]].clear();
}
storelatest.clear();
}
};
struct custom_hash{
static uint64_t splitmix64(uint64_t x){
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t a) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(a + FIXED_RANDOM);
}
template<class T> size_t operator()(T a) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
hash<T> x;
return splitmix64(x(a) + FIXED_RANDOM);
}
template<class T, class H> size_t operator()(pair<T, H> a) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
hash<T> x;
hash<H> y;
return splitmix64(x(a.f) * 37 + y(a.s) + FIXED_RANDOM);
}
};
template<class T, class H>using umap=unordered_map<T,H,custom_hash>;
int sz[MAXN], maxsz[MAXN], n, k;
vector<pair<int,int> >adj[MAXN];
unordered_map<int,int> f[MAXN];
const int MAXK = 10000010;
int exist[MAXK], exist2[MAXK];
int ans = 1e9;
int whole_size;
int number_of_operations = 0;
int dfs0(int node,int prev){
sz[node]=1;
number_of_operations++;
for(pair<int,int>x:adj[node]){
if(x.se==-1)continue;
if(x.fi==prev)continue;
int d=dfs0(x.fi,node);
sz[node]+=d;
}
return sz[node];
}
int dfs(int node,int prev){
sz[node]=1;
maxsz[node]=0;
number_of_operations++;
for(pair<int,int> x:adj[node]){
if(x.se==-1) continue;
if(x.fi==prev) continue;
int d=dfs(x.fi,node);
sz[node]+=d;
maxsz[node]=max(maxsz[node],d);
}
maxsz[node]=max(maxsz[node],whole_size-sz[node]);
return sz[node];
}
queue<int>ntv;
vector<int>all;
void wheewhoowhee(int node,int prev){
all.pb(node);
for(pair<int,int>x:adj[node]){
if(x.se==-1)continue;
if(x.fi==prev)continue;
wheewhoowhee(x.fi,node);
}
}
int divide(){
all.clear();
wheewhoowhee(ntv.front(),-1);
for(int i:all){
sz[i]=0;
maxsz[i]=1e9;
number_of_operations++;
}
whole_size=dfs0(ntv.front(),-1);
dfs(ntv.front(),-1);
ntv.pop();
int centroid=0, e=1e9;
for(int i:all){
if(e>maxsz[i]){
e=maxsz[i];
centroid=i;
}
}
for(pair<int,int> x:adj[centroid]){
if(x.se==-1) continue;
ntv.push(x.fi);
}
return centroid;
}
queue<int>used, used2, used3;
void dfs2(int node,int prev,int cur,int dep){
// cout <<cur <<"\n";
if(cur>=1 && cur<MAXK && exist2[cur]==1e9){
// cout << "FUCK\n";
used.push(cur);
used3.push(cur);
}
if(cur>=1 && cur<MAXK){
exist2[cur]=min(exist2[cur],dep);
}
for(pair<int,int>x:adj[node]){
if(x.se==-1) continue;
if(x.fi==prev) continue;
dfs2(x.fi,node,cur+x.se,dep+1);
}
}
void conquer(int root){
while(used2.size()){
exist[used2.front()]=1e9;
used2.pop();
}
for(int i=0;i<adj[root].size();i++){
if(adj[root][i].se==-1) continue;
int sto=adj[root][i].se;
adj[root][i].se=-1;
adj[adj[root][i].fi][f[adj[root][i].fi][root]].se=-1;
dfs2(adj[root][i].fi,-1,sto,1);
while(used3.size()){
// cout << "E "<<i<<" "<<used3.front()<<"\n";
if(k==used3.front()){
ans=min(ans,exist2[used3.front()]);
}
if(k-used3.front()>=1 && k-used3.front()<MAXK && exist[k-used3.front()]!=1e9){
// cout << "F "<<exist[k-used3.front()] << " " << exist2[used3.front()] << "\n";
ans=min(ans,exist[k-used3.front()]+exist2[used3.front()]);
// cout << "G "<<ans << "\n";
}
used3.pop();
}
while(used.size()){
if(exist[used.front()]==1e9) used2.push(used.front());
exist[used.front()]=min(exist[used.front()],exist2[used.front()]);
// cout << "exist "<<used.front()<<" "<<exist[used.front()]<<"\n";
exist2[used.front()]=1e9;
used.pop();
}
}
}
signed best_path(signed N,signed K,signed h[][2],signed l[]){
int n=N, k=K;
for(int i=1;i<=n;i++) exist[i]=1e9, exist2[i]=1e9;
for(int i=1;i<n;i++){
int u=h[i-1][0],v=h[i-1][1],w=l[i-1];
//cin >> u >> v >> w;
u++, v++;
int U=adj[u].size();
int V=adj[v].size();
f[u][v]=U;
f[v][u]=V;
adj[u].pb({v,w});
adj[v].pb({u,w});
}
ntv.push(1);
while(ntv.size()){
conquer(divide());
}
return (ans==1e9 ? -1 : ans);
}
