#include <bits/stdc++.h>
#pragma GCC optimize ("O3")
#pragma GCC optimize ("unroll-loops")
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define Submit
#ifdef Submit
#include "fun.h"
#endif // Submit
using namespace __gnu_pbds;
using namespace std;
template <typename T>
using ordered_set = tree <T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update>;
mt19937 gen(std :: chrono :: system_clock :: now().time_since_epoch().count());
#ifndef Submit
static void wrongAnswer(std::string message) {
printf("WA: %s\n", message.c_str());
exit(0);
}
namespace tree_helper {
static int _N;
static int logN;
static std::vector<std::vector<int>> parent;
static std::vector<int> depth;
static std::vector<int> subtree_size;
static void dfs(
const std::vector<std::vector<int>>& adj_list,
int current_node, int parent_node) {
parent[0][current_node] = parent_node;
subtree_size[current_node] = 1;
for (int i = 0; i < static_cast<int>(adj_list[current_node].size()); ++i) {
const int next_node = adj_list[current_node][i];
if (next_node != parent_node) {
depth[next_node] = depth[current_node] + 1;
dfs(adj_list, next_node, current_node);
subtree_size[current_node] += subtree_size[next_node];
}
}
}
static void initializeTree(const std::vector<std::vector<int>>& adj_list) {
_N = static_cast<int>(adj_list.size());
depth = std::vector<int>(_N, 0);
subtree_size = std::vector<int>(_N, 0);
for (logN = 0; (1 << logN) < _N; ++logN) {}
parent = std::vector<std::vector<int>>(logN, std::vector<int>(_N, 0));
dfs(adj_list, 0, 0);
for (int i = 1; i < logN; ++i) {
for (int j = 0; j < _N; ++j) {
parent[i][j] = parent[i - 1][parent[i - 1][j]];
}
}
}
static int getLowestCommonAncestor(int X, int Y) {
if (depth[X] < depth[Y]) {
std::swap(X, Y);
}
for (int i = logN - 1; i >= 0; --i) {
if (depth[parent[i][X]] >= depth[Y]) {
X = parent[i][X];
}
}
if (X == Y) {
return X;
}
for (int i = logN - 1; i >= 0; --i) {
if (parent[i][X] != parent[i][Y]) {
X = parent[i][X];
Y = parent[i][Y];
}
}
return parent[0][X];
}
static int getDistance(int X, int Y) {
return depth[X] + depth[Y] - 2 * depth[getLowestCommonAncestor(X, Y)];
}
static int attractionsBehind(int X, int Y) {
if (X == Y) {
return _N;
}
for (int i = logN - 1; i >= 0; --i) {
if (depth[parent[i][X]] > depth[Y]) {
X = parent[i][X];
}
}
if (Y == parent[0][X]) {
return _N - subtree_size[X];
}
return subtree_size[Y];
}
static void checkFunTour(const std::vector<int>& fun_tour) {
if (static_cast<int>(fun_tour.size()) != _N) {
wrongAnswer("Invalid size");
}
std::vector<bool> visited_attractions(_N, false);
for (int i = 0; i < _N; ++i) {
if (fun_tour[i] < 0 || fun_tour[i] >= _N) {
wrongAnswer("Invalid index");
}
if (visited_attractions[fun_tour[i]]) {
wrongAnswer("Repeated index");
}
visited_attractions[fun_tour[i]] = true;
}
int last_travel_time = getDistance(fun_tour[0], fun_tour[1]);
for (int i = 2; i < _N; ++i) {
int travel_time = getDistance(fun_tour[i - 1], fun_tour[i]);
if (travel_time > last_travel_time) {
wrongAnswer("Tour is not fun");
}
last_travel_time = travel_time;
}
}
} // namespace tree_helper
static int _N, Q;
int hoursRequired(int X, int Y) {
if (--Q < 0) {
wrongAnswer("Too many queries");
}
if (X < 0 || X >= _N || Y < 0 || Y >= _N) {
wrongAnswer("Invalid index");
}
return tree_helper::getDistance(X, Y);
}
int attractionsBehind(int X, int Y) {
if (--Q < 0) {
wrongAnswer("Too many queries");
}
if (X < 0 || X >= _N || Y < 0 || Y >= _N) {
wrongAnswer("Invalid index");
}
return tree_helper::attractionsBehind(X, Y);
}
#endif // Submit
const int N = 1e5 + 10;
int n;
int d[N];
vector <pair <int, int> > s[3];
vector <int> createFunTour(int _n, int _) {
n = _n;
int c = 0;
int minsz = 1e9;
for (int i = 0; i < n; ++i) {
int sz = attractionsBehind(0, i);
if (sz >= (n + 1) / 2 && sz < minsz) {
minsz = sz;
c = i;
}
}
vector <int> branches;
for (int i = 0; i < n; ++i) d[i] = hoursRequired(i, c);
for (int i = 0; i < n; ++i) if (d[i] == 1) branches.push_back(i);
for (int i = 0; i < n; ++i) {
if (i == c) continue;
int found = 0;
for (int j = 0; j < branches.size() - 1; ++j) {
if (hoursRequired(i, branches[j]) + 1 == d[i]) {
s[j].push_back({d[i], i});
found = 1;
break;
}
}
// if (i == 4) cout << found << "afdsdf\n";
if (!found) s[branches.size() - 1].push_back({d[i], i});
}
for (int i = 0; i < branches.size(); ++i) sort(s[i].begin(), s[i].end());
vector <int> ans;
int cur_branch = -1;
// for (int i = 0; i < branches.size(); ++i) {
// for (auto x: s[i]) cout << i << ' ' << x.first << ' ' << x.second << "aaa\n";
// }
for (int T = 0; T + 1 < n; ++T) {
int maxsz = 0, b = 0, tot = 0;
pair <int, int> farthest = {-1, -1};
for (int i = 0; i < branches.size(); ++i) {
if (s[i].size() > maxsz) {
maxsz = s[i].size();
b = i;
}
tot += s[i].size();
}
if (maxsz * 2 >= tot) {
int cur = 0;
int szbig = maxsz, szsmall = tot - szbig;
if (cur_branch == -1 || szbig != szsmall) {
cur = (szbig < szsmall);
} else {
int othersmall = -1;
for (int i = 0; i < branches.size(); ++i)
if (i != cur_branch && i != b) othersmall = i;
assert(othersmall != -1);
if (s[othersmall].size() && s[othersmall].back().first > d[ans.back()]) {
ans.push_back(s[othersmall].back().second);
s[othersmall].pop_back();
}
cur = 0;
}
vector <pair <int, int> > p[2];
p[0] = s[b];
for (int i = 0; i < branches.size(); ++i)
if (i != b) {
for (auto x: s[i]) p[1].push_back(x);
}
sort(p[1].begin(), p[1].end());
while (p[0].size() || p[1].size()) {
ans.push_back(p[cur].back().second);
p[cur].pop_back();
cur ^= 1;
}
break;
}
for (int i = 0; i < branches.size(); ++i) {
if (i == cur_branch) continue;
if (s[i].size()) farthest = max(farthest, make_pair(s[i].back().first, i));
}
int i = farthest.second;
cur_branch = i;
ans.push_back(s[i].back().second);
s[i].pop_back();
}
ans.push_back(c);
return ans;
}
#ifndef Submit
int main() {
freopen("test.inp", "r", stdin);
assert(2 == scanf("%d %d", &_N, &Q));
std::vector<std::vector<int>> adj_list(_N);
for (int i = 0; i < _N - 1; ++i) {
int A, B;
assert(2 == scanf("%d %d", &A, &B));
adj_list[A].push_back(B);
adj_list[B].push_back(A);
}
tree_helper::initializeTree(adj_list);
std::vector<int> fun_tour = createFunTour(_N, Q);
tree_helper::checkFunTour(fun_tour);
for (int i = 0; i < _N; ++i) {
printf("%d%c", fun_tour[i], " \n"[i == _N - 1]);
}
return 0;
}
#endif // Submit
/*
9 100000
0 1
1 2
1 3
3 4
4 6
6 5
6 7
7 8
*/
