#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll INF64 = (1LL<<62);
struct Edge{int to; ll w;};
struct TreeCenters{
int n, LOG;
vector<vector<Edge>> g;
vector<vector<int>> up;
vector<vector<ll>> jump;
vector<int> dep;
TreeCenters(int N, vector<vector<Edge>>&adj): n(N), g(adj){
LOG=1; while((1<<LOG)<=n) ++LOG;
up.assign(LOG, vector<int>(n+1,0));
jump.assign(LOG, vector<ll>(n+1,0));
dep.assign(n+1,0);
build(1,0,0);
for(int k=1;k<LOG;++k)
for(int v=1;v<=n;++v) if(up[k-1][v]){
up[k][v]=up[k-1][ up[k-1][v] ];
jump[k][v]=jump[k-1][v]+jump[k-1][ up[k-1][v] ];
}
}
void build(int v,int p,ll w){
up[0][v]=p; jump[0][v]=w;
for(auto e:g[v]) if(e.to!=p){
dep[e.to]=dep[v]+1;
build(e.to,v,e.w);
}
}
int climb(int v,ll R){
ll d=0;
for(int k=LOG-1;k>=0;--k)
if(up[k][v] && d + jump[k][v] <= R){
d+=jump[k][v];
v=up[k][v];
}
return v;
}
vector<int> centers(ll R){
vector<int> ord(n); iota(ord.begin(),ord.end(),1);
sort(ord.begin(),ord.end(),[&](int a,int b){return dep[a]>dep[b];});
vector<char> covered(n+1,0);
vector<int> cen;
deque<pair<int,ll>> dq;
for(int v:ord) if(!covered[v]){
int c=climb(v,R); cen.push_back(c);
dq.clear(); dq.push_back({c,0});
while(!dq.empty()){
auto [x,d]=dq.front(); dq.pop_front();
if(covered[x]) continue; covered[x]=1;
for(auto e:g[x]) if(!covered[e.to] && d+e.w<=R)
dq.push_back({e.to,d+e.w});
}
}
return cen;
}
};
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n,k; if(!(cin>>n>>k)) return 0;
vector<vector<Edge>> adj(n+1);
ll hi=0;
for(int i=0;i<n-1;++i){
int a,b; ll w; cin>>a>>b>>w;
adj[a].push_back({b,w});
adj[b].push_back({a,w});
hi+=w;
}
TreeCenters tc(n,adj);
ll lo=0, ansR=hi;
vector<int> ansC;
while(lo<=hi){
ll mid=(lo+hi)/2;
auto tmp=tc.centers(mid);
if((int)tmp.size()<=k){
ansR=mid; ansC.swap(tmp); hi=mid-1;
}else lo=mid+1;
}
ansC=tc.centers(ansR); // thu lại cho bán kính tối ưu
vector<char> mark(n+1,0);
for(int x:ansC) mark[x]=1;
for(int i=1;i<=n && (int)ansC.size()<k;++i)
if(!mark[i]) ansC.push_back(i);
cout<<ansR<<"\n";
for(int i=0;i<k;++i) cout<<(i?" ":"")<<ansC[i];
cout<<"\n";
return 0;
}
