#include<bits/stdc++.h>
#ifndef LOCAL
#include "fun.h"
#endif
#define ld long double
#define ll long long
#define pb push_back
const int INF = 1e9;
using namespace std;
#ifdef LOCAL
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
vector<int> createFunTour(int n, int q) {
if (n == 2) {
return vector<int>{0, 1};
}
int r = 0, len = INF;
for (int i = 1; i < n; i++) {
int val = attractionsBehind(0, i);
if (val > n / 2 && val < len) {
r = i;
len = val;
}
}
vector<int> d(n), one;
for (int i = 0; i < n; i++) {
if (i == r) continue;
d[i] = hoursRequired(i, r);
if (d[i] == 1) {
one.pb(i);
}
}
int sz = one.size();
vector<set<pair<int,int>>> st(sz);
for (int i = 0; i < n; i++) {
if (i == r) continue;
for (int j = 0; j < sz; j++) {
if (j + 1 == sz) {
st[j].insert({d[i], i});
} else {
if (hoursRequired(one[j], i) + 1 == d[i]) {
st[j].insert({d[i], i});
break;
}
}
}
}
int last = -1;
vector<int> p;
if (sz == 3) {
while (1) {
int sum = 0, mx = -1, j = -1;
for (int i = 0; i < 3; i++) {
sum += st[i].size();
if ((int)st[i].size() > mx) {
mx = st[i].size();
j = i;
}
}
if (mx >= sum - mx) {
vector<set<pair<int,int>>> stt(2);
if (last != -1) {
if (last == j) {
last = 1;
} else {
for (int k = 0; k < 3; k++) {
if (k != j && k != last) {
if (st[k].size() > 0 && st[last].size() > 0 && st[k].rbegin()->first > st[last].rbegin()->first) {
p.pb(st[k].rbegin()->second);
st[k].erase(*st[k].rbegin());
}
}
}
last = 0;
}
}
for (int k = 0; k < 3; k++) {
if (k != j) {
for (auto to : st[k]) {
stt[0].insert(to);
}
} else {
stt[1] = st[k];
}
}
st = stt;
break;
}
mx = -1, j = -1;
for (int i = 0; i < 3; i++) {
if (st[i].size() == 0 || i == last) continue;
if (st[i].rbegin()->first > mx) {
mx = st[i].rbegin()->first;
j = i;
}
}
p.pb(st[j].rbegin()->second);
st[j].erase(*st[j].rbegin());
last = j;
}
}
if (last == -1) {
if (st[0].size() > st[1].size()) {
last = 1;
} else {
last = 0;
}
}
while (st[0].size() > 0 || st[1].size() > 0) {
if (last == 0) {
p.pb(st[1].rbegin()->second);
st[1].erase(*st[1].rbegin());
} else {
p.pb(st[0].rbegin()->second);
st[0].erase(*st[0].rbegin());
}
last ^= 1;
}
p.pb(r);
return p;
}
#ifdef LOCAL
int main() {
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
