// --------------------------------------------------<TEMPLATE>--------------------------------------------------
// --------------------<optimizations>--------------------
#pragma GCC optimize("O3")
//(UNCOMMENT WHEN HAVING LOTS OF RECURSIONS)\
#pragma comment(linker, "/stack:200000000")
//(UNCOMMENT WHEN NEEDED)\
#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector,fast-math")\
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// -------------------</optimizations>--------------------
// ---------------<Headers and namespaces>----------------
#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <ratio>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>
using namespace __gnu_pbds;
using namespace __gnu_cxx;
*/
// ---------------</Headers and namespaces>---------------
// -----------------<Defines and typedefs>----------------
// typedef tree<int,null_type,less<int>,rb_tree_tag, \
tree_order_statistics_node_update> indexed_set; // use less_equal for multiset
// order_of_key (val): returns the no. of values less than val
// find_by_order (k): returns the iterator to kth largest element.(0-based)
typedef long double LD;
typedef long long ll;
#define int ll
#define pb push_back
#define mp make_pair
#define REP(i,n) for (int i = 0; i < n; i++)
#define FOR(i,a,b) for (int i = a; i < b; i++)
#define REPD(i,n) for (int i = n-1; i >= 0; i--)
#define FORD(i,a,b) for (int i = a; i >= b; i--)
#define remax(a,b) a = max(a,b)
#define remin(a,b) a = min(a,b)
#define all(v) v.begin(),v.end()
typedef map<int,int> mii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int,int> pii;
typedef vector<pii> vpii;
#define F first
#define S second
#define PQ(type) priority_queue<type>
#define PQD(type) priority_queue<type,vector<type>,greater<type> >
#define ITR :: iterator it
#define WL(t) while(t --)
#define SZ(x) ((int)(x).size())
#define runtime() ((double)clock() / CLOCKS_PER_SEC)
#define TR(container,it) for(typeof(container.begin()) it=container.begin();it!=container.end();it++)
#define sqr(x) ((x)*(x))
#define inrange(i,a,b) ((i>=min(a,b)) && (i<=max(a,b)))
// -----<SCANF>-----
#define sfi(x) scanf("%d",&x);
#define sfi2(x,y) scanf("%d%d",&x,&y);
#define sfi3(x,y,z) scanf("%d%d%d",&x,&y,&z);
#define sfl(x) scanf("%lld",&x);
#define sfl2(x,y) scanf("%lld%lld",&x,&y);
#define sfl3(x,y,z) scanf("%lld%lld%lld",&x,&y,&z);
#define sfl4(x,y,z,x1) scanf("%lld%lld%lld%lld",&x,&y,&z,&x1);
#define sfl5(x,y,z,x1,y1) scanf("%lld%lld%lld%lld%lld",&x,&y,&z,&x1,&y1);
#define sfl6(x,y,z,x1,y1,z1) scanf("%lld%lld%lld%lld%lld%lld",&x,&y,&z,&x1,&y1,&z1);
#define sfs(x) scanf("%s",x);
#define sfs2(x,y) scanf("%s%s",x,y);
#define sfs3(x,y,z) scanf("%s%s%s",x,y,z);
// ----</SCANF>-----
// ----<PRINTF>-----
#define pfi(x) printf("%d\n",x);
#define pfi2(x,y) printf("%d %d\n",x,y);
#define pfi3(x,y,z) printf("%d %d %d\n",x,y,z);
#define pfl(x) printf("%lld\n",x);
#define pfl2(x,y) printf("%lld %lld\n",x,y);
#define pfl3(x,y,z) printf("%lld %lld %lld\n",x,y,z);
#define pfs(x) printf("%s\n",x);
#define pfs2(x,y) printf("%s %s\n",x,y);
#define pfs3(x,y,z) printf("%s %s %s\n",x,y,z);
#define pwe(x) printf("%lld ",x); // print without end
// ----</PRINTF>----
#define FLSH fflush(stdout)
#define fileIO(name) \
freopen(name".in", "r", stdin); \
freopen(name".out", "w", stdout);
#define PRECISION(x) cout << fixed << setprecision(x);
#define FAST_IO ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
// ----------------</Defines and typedefs>----------------
// -------------------<Debugging stuff>-------------------
#define TRACE
#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
const char* comma = strchr(names + 1, ',');cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}
#else
#define trace(...)
#endif
// ------------------</Debugging stuff>-------------------
// ------------------------<Consts>-----------------------
const int MAXN = 1000005;
const int SQRTN = 1003;
const int LOGN = 22;
const double PI=acos(-1);
#ifdef int
const int INF=1e16;
#else
const int INF=1e9;
#endif
const int MOD = 1000000007;
const int FMOD = 998244353;
const double eps = 1e-9;
// -----------------------</Consts>-----------------------
// -------------------------<RNG>-------------------------
mt19937 RNG(chrono::steady_clock::now().time_since_epoch().count());
#define SHUF(v) shuffle(all(v), RNG);
// Use mt19937_64 for 64 bit random numbers.
// ------------------------</RNG>-------------------------
// ----------------------<MATH>---------------------------
template<typename T> T gcd(T a, T b){return(b?__gcd(a,b):a);}
template<typename T> T lcm(T a, T b){return(a*(b/gcd(a,b)));}
int add(int a, int b, int c = MOD){int res=a+b;return(res>=c?res-c:res);}
int mod_neg(int a, int b, int c = MOD){int res;if(abs(a-b)<c)res=a-b;else res=(a-b)%c;return(res<0?res+c:res);}
int mul(int a, int b, int c = MOD){ll res=(ll)a*b;return(res>=c?res%c:res);}
int muln(int a, int b, int c = MOD){ll res=(ll)a*b;return ((res%c)+c)%c;}
ll mulmod(ll a,ll b, ll m = MOD){ll q = (ll)(((LD)a*(LD)b)/(LD)m);ll r=a*b-q*m;if(r>m)r%=m;if(r<0)r+=m;return r;}
template<typename T>T expo(T e, T n){T x=1,p=e;while(n){if(n&1)x=x*p;p=p*p;n>>=1;}return x;}
template<typename T>T power(T e, T n, T m = MOD){T x=1,p=e;while(n){if(n&1)x=mul(x,p,m);p=mul(p,p,m);n>>=1;}return x;}
template<typename T>T extended_euclid(T a, T b, T &x, T &y){T xx=0,yy=1;y=0;x=1;while(b){T q=a/b,t=b;b=a%b;a=t;\
t=xx;xx=x-q*xx;x=t;t=yy;yy=y-q*yy;y=t;}return a;}
template<typename T>T mod_inverse(T a, T n = MOD){T x,y,z=0;T d=extended_euclid(a,n,x,y);return(d>1?-1:mod_neg(x,z,n));}
const int FACSZ = 1; // Make sure to change this
int fact[FACSZ],ifact[FACSZ];
void precom(int c = MOD){
fact[0] = 1;
FOR(i,1,FACSZ) fact[i] = mul(fact[i-1],i,c);
ifact[FACSZ-1] = mod_inverse(fact[FACSZ-1],c);
REPD(i,FACSZ-1){
ifact[i] = mul(i+1,ifact[i+1],c);
}
}
int ncr(int n,int r,int c = MOD){
return mul(mul(ifact[r],ifact[n-r],c),fact[n],c);
}
// ----------------------</MATH>--------------------------
// --------------------------------------------------</TEMPLATE>--------------------------------------------------
// void solvethetestcase();
// signed main(){
// // (UNCOMMENT FOR CIN/COUT) \
// FAST_IO
// PRECISION(10)
// int t = 1;
// // (UNCOMMENT FOR MULTIPLE TEST CASES) \
// sfl(t);
// FOR(testcase,1,t+1){
// // (UNCOMMENT FOR CODEJAM) \
// printf("Case #%lld: ",testcase);
// solvethetestcase();
// }
// }
int n,k;
vpii adj[200005];
pii par[200005][21];
int dep[200005],sz[200005];
void dfs(int u,int p,int pw,int d){
dep[u] = d;
par[u][0] = {p,pw};
sz[u] = 1;
for(auto v:adj[u]){
if(v.F != p){
dfs(v.F,u,v.S,d+1);
sz[u] += sz[v.F];
}
}
}
int root = -1;
bitset<200005> vis;
int cen_par[200005];
vi cen_adj[200005];
vector<pair<pii,int> > lmao[200005],lmao2;
void dfs_cen(int u,int last,int tot){
// trace(u,last,tot);
int flag = 1;
for(auto v:adj[u]){
if(vis[v.F]) continue;
if(v.F == par[u][0].F){
if(tot-sz[u] > tot/2){
flag = 0;
dfs_cen(v.F,last,tot);
break;
}
}
else{
if(sz[v.F] > tot/2){
flag = 0;
dfs_cen(v.F,last,tot);
break;
}
}
}
if(flag){
if(last == -1){
root = u;
}
else{
cen_adj[last].pb(u);
cen_par[u] = last;
}
vis[u] = 1;
for(auto v:adj[u]){
if(vis[v.F]) continue;
if(v.F == par[u][0].F) dfs_cen(v.F,u,tot-sz[u]);
else dfs_cen(v.F,u,sz[v.F]);
}
}
}
pii lca_dist(int u,int v){
if(dep[u] > dep[v]) swap(u,v);
int res1 = 0,res2 = 0;
FORD(j,20,0){
if(dep[v]-(1<<j) >= dep[u]){
res1 += par[v][j].S;
v = par[v][j].F;
res2 += (1<<j);
}
}
if(u == v) return {res1,res2};
FORD(j,20,0){
if(par[u][j].F != par[v][j].F){
res1 += par[u][j].S+par[v][j].S;
res2 += (1<<j)+(1<<j);
u = par[u][j].F;
v = par[v][j].F;
}
}
res1+=par[u][0].S+par[v][0].S;
res2 += 2;
return {res1,res2};
}
signed best_path(signed N,signed K,signed H[][2],signed L[]){
n = N;
k = K;
REP(i,N-1){
int u = H[i][0],v = H[i][1],w = L[i];
adj[u].pb({v,w});
adj[v].pb({u,w});
}
dfs(0,0,0,0);
FOR(j,1,21){
REP(i,n){
par[i][j] = {par[par[i][j-1].F][j-1].F,par[i][j-1].S+par[par[i][j-1].F][j-1].S};
}
}
vis.reset();
dfs_cen(0,-1,N);
REP(i,n){
int cur = i;
while(cur != root){
lmao[cen_par[cur]].pb({lca_dist(cen_par[cur],i),cur});
cur = cen_par[cur];
}
}
REP(i,n) sort(all(lmao[i]));
signed res = n+5;
REP(i,n){
lmao2.clear();
REP(j,lmao[i].size()){
if(lmao[i][j].F.F == k) remin(res,(signed)lmao[i][j].F.S);
if(j > 0 and lmao[i][j].F.F == lmao[i][j-1].F.F and lmao[i][j].S == lmao[i][j-1].S) continue;
lmao2.pb(lmao[i][j]);
}
REP(j,lmao2.size()){
pair<pii,int> bkl = {{k-lmao2[j].F.F,-1},-1};
int ind = lower_bound(all(lmao2),bkl)-lmao2.begin();
if(ind < lmao2.size() and lmao2[ind].F.F+lmao2[j].F.F == k and lmao2[ind].S != lmao2[j].S) remin(res,(signed)lmao2[ind].F.S+(signed)lmao2[j].F.S);
ind++;
if(ind < lmao2.size() and lmao2[ind].F.F+lmao2[j].F.F == k and lmao2[ind].S != lmao2[j].S) remin(res,(signed)lmao2[ind].F.S+(signed)lmao2[j].F.S);
}
}
if(res == n+5) return -1;
return res;
}
// void solvethetestcase(){
// signed N,K;
// sfi2(N,K);
// signed H[N-1][2],L[N-1];
// REP(i,N-1){
// sfi3(H[i][0],H[i][1],L[i])
// }
// pfi(best_path(N,K,H,L))
// }
