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 ll long long
#define pb push_back
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
#define sz(x) (int)x.size()
#define fi first
#define sd second
#define all(x) x.begin(), x.end()
//#pragma GCC target ("avx2")
//#pragma GCC optimization ("O3")
//#pragma GCC optimization ("unroll-loops")
using namespace std;
//using namespace __gnu_pbds;
//typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
const int N = (int)2e5 + 500;
vector< pair<int, int> > g[N];
ll dp_down[N], dp_up[N], cur;
int n, k;
vector<int> ans;
bool used[N];
void dfs(int v, int pr, ll d)
{
dp_down[v] = 1e18;
dp_up[v] = 0;
for(const auto &[u, w] : g[v])
{
if (u == pr) continue;
dfs(u, v, w);
dp_down[v] = min(dp_down[v], dp_down[u]);
dp_up[v] = max(dp_up[v], dp_up[u]);
}
if (dp_down[v] + dp_up[v] <= cur)
dp_up[v] = -1e18;
if (dp_up[v] != -1e18 && (pr == -1 || dp_up[v] + d > cur))
{
dp_down[v] = 0;
dp_up[v] = -1e18;
ans.pb(v);
}
dp_down[v] += d; dp_up[v] += d;
}
int main()
{
ios_base::sync_with_stdio(0); cin.tie(0);
cin >> n >> k;
for(int i = 1; i < n; i++)
{
int u, v, w;
cin >> u >> v >> w;
g[u].pb({v, w});
g[v].pb({u, w});
}
ll l = 0, r = 2e14;
while(l < r)
{
ll m = (l + r) / 2ll;
cur = m;
ans.clear();
dfs(1, -1, 0);
if (sz(ans) <= k) r = m;
else l = m + 1;
}
cur = l;
ans.clear();
dfs(1, -1, 0);
cout << l << '\n';
for(auto &u : ans) used[u] = 1;
for(int i = 1; i <= n; i++)
if (sz(ans) < k && !used[i])
{
ans.pb(i);
}
for(auto u : ans) cout << u << ' ';
}
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