#pragma GCC optimize("Ofast,no-stack-protector")
#pragma GCC target("avx") 
#pragma GCC optimize("Ofast")
#pragma GCC optimize ("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

#include "bits/stdc++.h"
#define MAXN 100009
#define INF 1000000007
#define mp(x,y) make_pair(x,y)
#define all(v) v.begin(),v.end()
#define pb(x) push_back(x)
#define wr cout<<"----------------"<<endl;
#define ppb() pop_back()
#define tr(ii,c) for(__typeof((c).begin()) ii=(c).begin();ii!=(c).end();ii++)
#define ff first
#define ss second
#define my_little_dodge 46
#define debug(x)  cerr<< #x <<" = "<< x<<endl;
using namespace std;

typedef long long ll;
typedef pair<int,int> PII;
template<class T>bool umin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<class T>bool umax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
int a[MAXN],b[MAXN],n,dp[MAXN];
int sub[MAXN],F[MAXN*2];
vector<int>adj[MAXN];
vector<PII>way[MAXN];
void upd(int x,int val){
	for(;x<MAXN*2;x+=x&(-x))
		F[x]+=val;
}
int tap(int x){
	int res=0;
	for(;x;x-=x&(-x))
		res+=F[x];
	return res;	
}
int add(int nd,int root){
	//~ cout<<"add "<<nd<<endl;
	int res=(a[nd]<=b[root]);
	tr(it,adj[nd])
		res+=add(*it,root);
	return res;	
}
void update(int nd,int val){
	//~ cout<<"del "<<nd<<endl;
	upd(a[nd],val);
	tr(it,adj[nd])
		update(*it,val);
}
ll dfs(int nd,bool keep){
	int mx=-1,who=-1;
	for(int i=0;i<int(adj[nd].size());i++){
		int to=adj[nd][i];
		if(umax(mx,sub[to]))
			who=to;
	}
	ll ans=0;	
	for(int i=0;i<int(adj[nd].size());i++){
		int to=adj[nd][i];
		if(to==who)
			continue;
		ans+=dfs(to,0);	
	}
	if(~who)
		ans+=dfs(who,1);
	ans+=tap(b[nd]);	
	for(int i=0;i<int(adj[nd].size());i++){
		int to=adj[nd][i];
		if(to==who)
			continue;
		ans+=add(to,nd);
	}
	if(keep){
		upd(a[nd],+1);
		for(int i=0;i<int(adj[nd].size());i++){
			int to=adj[nd][i];
			if(to==who)
				continue;
			update(to,+1);	
		}
	}
	else{
		if(~who)
			update(who,-1);
	}
	return ans;
}

ll solve(int x){
	vector<PII>v;
	for(int i=1;i<=n;i++)	
		v.pb(mp(dp[i],i));
	for(int i=1;i<=n;i++)
		v.pb(mp(dp[i]+x,i+n));
	sort(all(v));int now=1;
	for(int i=0;i<int(v.size());i++){
		if(i and v[i].ff!=v[i-1].ff)
			now++;
		if(v[i].ss>n)
			b[v[i].ss-n]=now;
		else
			a[v[i].ss]=now;
	}
	return dfs(1,0);
}
void travel(int nd,int pr){
	sub[nd]=1;
	for(int i=0;i<int(way[nd].size());i++){
		int to=way[nd][i].ff;
		int c=way[nd][i].ss;
		if(to==pr)
			continue;
		dp[to]=dp[nd]+c;	
		adj[nd].pb(to);	
		travel(to,nd);	
		sub[nd]+=sub[to];
	}
}
int main(){
    //~ freopen("file.in", "r", stdin);
    scanf("%d",&n);
    ll k;
    scanf("%lld",&k);
    for(int i=2;i<=n;i++){
		int x,y,c;
		scanf("%d%d%d",&x,&y,&c);
		way[x].pb(mp(y,c));
		way[y].pb(mp(x,c));
	}
	travel(1,-1);
	int st=0,en=1e9;
	while(st+1<en){
		int mid=(st+en)>>1;
		if(solve(mid)<k)
			st=mid;
		else
			en=mid;
	}
	if(solve(st)>=k)
		printf("%d\n",st);
	else
		printf("%d\n",en);
	return 0;
}