The nation of Panel holds an annual show called The Number Games, where each district in the nation will be represented by one contestant.

The nation has n districts numbered from 1 to n, each district has exactly one path connecting it to every other district. The number of fans of a contestant from district i is equal to 2^i.

This year, the president decided to reduce the costs. He wants to remove k contestants from the games. However, the districts of the removed contestants will be furious and will not allow anyone to cross through their districts. 

The president wants to ensure that all remaining contestants are from districts that can be reached from one another. He also wishes to maximize the total number of fans of the participating contestants.

Which contestants should the president remove?

Input

The first line of input contains two integers n and k (1 ≤ k < n ≤ 10^6) — the number of districts in Panel, and the number of contestants the president wishes to remove, respectively.

The next n-1 lines each contains two integers a and b (1 ≤ a, b ≤ n, a ≠ b), that describe a road that connects two different districts a and b in the nation. It is guaranteed that there is exactly one path between every two districts.

Output

Print k space-separated integers: the numbers of the districts of which the contestants should be removed, in increasing order of district number.

Examples

Input

6 3
2 1
2 6
4 2
5 6
2 3


Output

1 3 4


Input

8 4
2 6
2 7
7 8
1 2
3 1
2 4
7 5


Output

1 3 4 5

Note

In the first sample, the maximum possible total number of fans is 2^2 + 2^5 + 2^6 = 100. We can achieve it by removing the contestants of the districts 1, 3, and 4.
#include <bits/stdc++.h>
const int _ML = 228;
const char _inpf[] = "";
const char _outf[] = "";
#pragma GCC optimize("O3,no-stack-protector")
using namespace std;
const double PI = 3.14159265358979323846;
mt19937 rd(228);
template <class T, class U>
inline ostream &operator<<(ostream &, const pair<T, U> &);
template <class T, class U>
inline istream &operator>>(istream &, pair<T, U> &);
template <class T>
inline ostream &operator<<(ostream &, const vector<T> &);
template <class T>
inline istream &operator>>(istream &, vector<T> &);
template <class T>
inline ostream &operator<<(ostream &, const set<T> &);
template <class T>
inline ostream &operator<<(ostream &, const multiset<T> &);
template <class T>
inline ostream &operator<<(ostream &, const unordered_set<T> &);
template <class T>
inline ostream &operator<<(ostream &, const unordered_multiset<T> &);
template <class T, class U>
inline ostream &operator<<(ostream &, const map<T, U> &);
template <class T, class U>
inline ostream &operator<<(ostream &, const unordered_map<T, U> &);
const int N = 1000 * 1000 + 228;
const int L = 20;
vector<int> g[N];
bool clr[N];
int up[N][L];
void dfs(int v, int p) {
  up[v][0] = p;
  for (int i = 1; i < L; ++i) {
    if (up[v][i - 1] == -1) {
      up[v][i] = -1;
    } else {
      up[v][i] = up[up[v][i - 1]][i - 1];
    }
  }
  for (int i : g[v]) {
    if (i == p) {
      continue;
    }
    dfs(i, v);
  }
}
inline void _main_function() {
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    cin >> a >> b;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  dfs(n, -1);
  vector<int> ans;
  int cur = 1;
  clr[n] = true;
  for (int i = n - 1; i >= 1; --i) {
    if (clr[i]) {
      continue;
    }
    int len = 0;
    int v = i;
    for (int j = L - 1; j >= 0; --j) {
      if (up[v][j] != -1 && !clr[up[v][j]]) {
        len += (1 << j);
        v = up[v][j];
      }
    }
    v = up[v][0];
    ++len;
    if (cur + len > n - k) {
      ans.push_back(i);
      continue;
    }
    cur += len;
    for (int j = i; j != v; j = up[j][0]) {
      clr[j] = true;
    }
  }
  reverse((ans).begin(), (ans).end());
  cout << ans << '\n';
}
int main() {
  if (_inpf[0] != '\0') assert(freopen(_inpf, "r", stdin) != nullptr);
  if (_outf[0] != '\0') assert(freopen(_outf, "w", stdout) != nullptr);
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout << setprecision(20);
  _main_function();
}
template <class T, class U>
inline ostream &operator<<(ostream &_out, const pair<T, U> &_p) {
  _out << _p.first << ' ' << _p.second;
  return _out;
}
template <class T, class U>
inline istream &operator>>(istream &_in, pair<T, U> &_p) {
  _in >> _p.first >> _p.second;
  return _in;
}
template <class T>
inline ostream &operator<<(ostream &_out, const vector<T> &_v) {
  if (_v.empty()) {
    return _out;
  }
  _out << *_v.begin();
  for (auto _it = ++_v.begin(); _it != _v.end(); ++_it) {
    _out << ' ' << *_it;
  }
  return _out;
}
template <class T>
inline istream &operator>>(istream &_in, vector<T> &_v) {
  for (auto &_i : _v) {
    _in >> _i;
  }
  return _in;
}
template <class T>
inline ostream &operator<<(ostream &_out, const set<T> &_s) {
  if (_s.empty()) {
    return _out;
  }
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) {
    _out << ' ' << *_it;
  }
  return _out;
}
template <class T>
inline ostream &operator<<(ostream &_out, const multiset<T> &_s) {
  if (_s.empty()) {
    return _out;
  }
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) {
    _out << ' ' << *_it;
  }
  return _out;
}
template <class T>
inline ostream &operator<<(ostream &_out, const unordered_set<T> &_s) {
  if (_s.empty()) {
    return _out;
  }
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) {
    _out << ' ' << *_it;
  }
  return _out;
}
template <class T>
inline ostream &operator<<(ostream &_out, const unordered_multiset<T> &_s) {
  if (_s.empty()) {
    return _out;
  }
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) {
    _out << ' ' << *_it;
  }
  return _out;
}
template <class T, class U>
inline ostream &operator<<(ostream &_out, const map<T, U> &_m) {
  if (_m.empty()) {
    return _out;
  }
  _out << '(' << _m.begin()->first << ": " << _m.begin()->second << ')';
  for (auto _it = ++_m.begin(); _it != _m.end(); ++_it) {
    _out << ", (" << _it->first << ": " << _it->second << ')';
  }
  return _out;
}
template <class T, class U>
inline ostream &operator<<(ostream &_out, const unordered_map<T, U> &_m) {
  if (_m.empty()) {
    return _out;
  }
  _out << '(' << _m.begin()->first << ": " << _m.begin()->second << ')';
  for (auto _it = ++_m.begin(); _it != _m.end(); ++_it) {
    _out << ", (" << _it->first << ": " << _it->second << ')';
  }
  return _out;
}
