This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define pb push_back
#define F first
#define S second
#define sz(x) (int)x.size()
#define el "\n"
using namespace std;
typedef long long ll;
const int N = 2e5 + 500;
ll ans = 1e18;
int best, n, k;
vector <pair <int, int> > g[N];
ll dp[N];
ll d[25][25];
void dfs(int v, int pr) {
for (auto p : g[v]) {
int u = p.F, w = p.S;
if (u == pr) {
continue;
}
dfs(u, v);
dp[v] = max(dp[u] + w, dp[v]);
}
}
void go(int v, int pr, ll longest) {
multiset <ll> se;
for (auto u : g[v]) {
if (u.F == pr) {
continue;
}
se.insert(dp[u.F] + u.S);
}
if (max(longest, dp[v]) < ans) {
ans = max(longest, dp[v]);
best = v;
}
for (auto u : g[v]) {
if (u.F == pr) {
continue;
}
se.erase(se.find(dp[u.F] + u.S));
ll nlongest = longest;
if (sz(se)) {
nlongest = max(nlongest, *se.rbegin());
}
go(u.F, v, nlongest + u.S);
se.insert(dp[u.F] + u.S);
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(NULL);
cin >> n >> k;
for (int i = 1; i < n; i++) {
int u, v, w;
cin >> u >> v >> w; u--; v--;
g[v].pb({u, w});
g[u].pb({v, w});
}
if (n <= 20) {
ll acur = 1e18;
vector <int> ans;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
d[i][j] = 1e18;
}
}
for (int i = 0; i < n; i++) {
for (auto j : g[i]) {
int w = j.S;
int u = j.F;
d[i][u] = w;
}
}
for (int m = 0; m < n; m++) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
d[i][j] = min(d[i][j], d[i][m] + d[m][j]);
}
}
}
for (int mask = 0; mask < (1 << n); mask++) {
if (__builtin_popcount(mask) != k) {
continue;
}
vector <int> cur;
for (int i = 0; i < n; i++) {
if (mask & (1 << i)) {
cur.pb(i);
}
}
ll mx = 0;
for (int i = 0; i < n; i++) {
if (!(mask & (1 << i))) {
ll mn = 1e18;
for (auto j : cur) {
mn = min(mn, d[i][j]);
}
mx = max(mx, mn);
}
}
if (mx < acur) {
acur = mx;
ans = cur;
}
}
cout << acur << el;
for (auto x : ans) {
cout << x + 1 << " ";
}
return 0;
}
dfs(0, -1);
go(0, -1, 0);
cout << ans << el << best + 1;
}
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