Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. The Number Games

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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 $$$k$$$ ($$$1 \leq k < n \leq 10^6$$$) — 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 $$$b$$$ ($$$1 \leq a, b \leq n$$$, $$$a \ne b$$$), 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.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/25/2019 01:18:57 (d3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|