#include<bits/stdc++.h>
using namespace std;
const int N=5e4+10;
inline int read()
{
	int s=0,w=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
	while(ch>='0'&&ch<='9')s=(s<<1)+(s<<3)+(ch^48),ch=getchar();
	return s*w;
}
int n,m,head[N],cnt,maxn,d1[N],d2[N],ans,f[N];
struct node{
	int to,net,u,val;
}e[N<<1];
multiset<int> s[N];
void add(int x,int y,int z)
{
	e[++cnt].to=y;e[cnt].net=head[x];head[x]=cnt;e[cnt].val=z;
}
int dfs1(int x,int fa)
{
	d1[x]=d2[x]=0;
	for(int i=head[x];i;i=e[i].net)
	{
		int to=e[i].to;
		if(to==fa)continue;
		dfs1(to,x);
		int t=d1[to]+e[i].val;
		if(t>d1[x])
		{
			d2[x]=d1[x];d1[x]=t;
		}else if(t>d2[x])
		{
			d2[x]=t;
		}
	}
	maxn=max(maxn,d1[x]+d2[x]);
}
int dfs2(int x,int fa,int mid)
{
	s[x].clear();
	for(int i=head[x];i;i=e[i].net)
	{
		int to=e[i].to;
		if(to==fa)continue;
		dfs2(to,x,mid);
		if(e[i].val+f[to]>=mid)ans++;
		else s[x].insert(f[to]+e[i].val);
	}
	while(!s[x].empty())
	{
		multiset<int>::iterator it1=s[x].begin();
		s[x].erase(it1);
		multiset<int>::iterator it2=s[x].lower_bound(mid-*it1);
		if(it2==s[x].end())
		{
			f[x]=max(f[x],*it1);
		}
		else 
		{
			ans++;s[x].erase(it2);
		}
	}
}
bool check(int mid)
{
	ans=0;memset(f,0,sizeof(f));
	dfs2(1,0,mid);
	if(ans>=m)return 1;
	else return 0;
}
signed main()
{
	n=read();m=read();
	for(int i=1;i<n;i++)
	{
		int x=read(),y=read(),w=read();
		add(x,y,w);add(y,x,w);
	}
	dfs1(1,0);
	int l=0,r=maxn;
	while(l<r)
	{
		int mid=(l+r+1)>>1;
		if(check(mid))l=mid;
		else r=mid-1;
	}
	cout<<l;
	return 0;
}