#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
int n, k, x, y, w, t = 0, up[20][200001], child[200001], par[200001], h[200001], st[21][400001], f[200001];
bool ok[200001], del[200001];
long long cnt, d[200001], sum[20][200001], best[200001], S;
vector<pair<int, int>> ke[200001];
vector<pair<long long, int>> a;
vector<int> ans;
vector<pair<int, long long>> path[200001];
void dfs(int u, int p){
for(auto [v, w] : ke[u]){
if(v == p) continue;
up[0][v] = u;
sum[0][v] = w;
h[v] = h[u] + 1;
for(int i = 1; i <= __lg(n); i++){
up[i][v] = up[i - 1][up[i - 1][v]];
sum[i][v] = sum[i - 1][v] + sum[i - 1][up[i - 1][v]];
}
d[v] = d[u] + w;
dfs(v, u);
}
}
void dfs2(int u, int p){
f[u] = ++t;
st[0][t] = u;
for(auto [v, w] : ke[u]){
if(v == p) continue;
dfs2(v, u);
t++;
st[0][t] = u;
}
}
void build2(){
for(int i = 1; i <= __lg(t); i++){
for(int j = 1; j <= t - (1 << i) + 1; j++){
x = st[i - 1][j];
y = st[i - 1][j + (1 << (i - 1))];
if(h[x] < h[y]) st[i][j] = x;
else st[i][j] = y;
}
}
}
int lca(int l, int r){
if(l > r) swap(l, r);
int k = __lg(r - l + 1);
x = st[k][l];
y = st[k][r - (1 << k) + 1];
if(h[x] < h[y]) return x;
else return y;
}
long long dist(int u, int v){
return d[u] + d[v] - 2 * d[lca(f[u], f[v])];
}
void countchild(int u, int p){
child[u] = 1;
for(auto [v, w] : ke[u]){
if(v == p || del[v]) continue;
countchild(v, u);
child[u] += child[v];
}
}
int centroid(int u, int p, int n){
for(auto [v, w] : ke[u]){
if(v != p && !del[v] && child[v] > n / 2) return centroid(v, u, n);
}
return u;
}
void collect(int u, int p, int cen, long long dist0){
path[u].push_back({cen, dist0});
for(auto [v, w] : ke[u]){
if(v == p || del[v]) continue;
collect(v, u, cen, dist0 + w);
}
}
int build(int u){
countchild(u, 0);
int n = child[u];
int root = centroid(u, 0, n);
del[root] = true;
collect(root, 0, root, 0);
for(auto [v, w] : ke[root]){
if(!del[v]){
int f = build(v);
par[f] = root;
}
}
return root;
}
int dat(int u){
long long cnt = 0;
for(int i = __lg(n); i >= 0; i--){
if(cnt + sum[i][u] <= S){
cnt += sum[i][u];
u = up[i][u];
if(u <= 1) return 1;
}
}
return u;
}
inline bool phu(int u){
for(auto [c, d0] : path[u]){
if(best[c] + d0 <= S) return true;
}
return false;
}
inline void upd(int u){
for(auto [c, d0] : path[u]){
best[c] = min(best[c], d0);
}
}
bool check(long long pp){
S = pp;
fill(best + 1, best + n + 1, (long long)4e18);
vector<int> now;
for(auto [ff, g] : a){
if(!phu(g)){
int r = dat(g);
now.push_back(r);
upd(r);
if((int)now.size() > k) return false;
}
}
ans = now;
return true;
}
int main(){
ios::sync_with_stdio(0);
cin.tie(nullptr);
cin >> n >> k;
for(int i = 1; i < n; i++){
cin >> x >> y >> w;
ke[x].push_back({y, w});
ke[y].push_back({x, w});
}
dfs(1, 0);
dfs2(1, 0);
build2();
build(1);
for(int i = 1; i <= n; i++) a.push_back({d[i], i});
sort(a.begin(), a.end(), greater<pair<long long, int>>());
long long vt = -1, l = 1, r = 2e14, mid;
while(l <= r){
mid = (l + r) / 2;
if(check(mid)){
vt = mid;
r = mid - 1;
}else l = mid + 1;
}
cout << vt << "\n";
for(int v : ans) ok[v] = true;
int m = (int)ans.size();
vector<int> nans;
for(int i = 1; i <= n; i++){
if(ok[i]) nans.push_back(i);
else if(m < k){
m++;
nans.push_back(i);
}
}
for(int j = 0; j < (int)nans.size() - 1; j++) cout << nans[j] << " ";
cout << nans.back();
return 0;
}
