[POI2011]IMP-Party

题目描述

```plain Byteasar intends to throw up a party. ``` Naturally, he would like it to be a success. Furthermore, Byteasar is quite certain that to make it so it suffices if all invited guests know each other. He is currently trying to come up with a list of his friends he would like to invite. Byteasar has $n$ friends, where $n$ is divisible by 3. ```plain Fortunately, most of Byteasar's friends know one another. ``` Furthermore, Byteasar recalls that he once attended a party where there were $\frac{2}{3}n$ of his friends, and where everyone knew everyone else. Unfortunately, Byteasar does not quite remember anything else from that party. In particular, he has no idea which of his friends attended it. Byteasar does not feel obliged to throw a huge party, but he would like to invite at least \frac{n}{3} of his friends. He has no idea how to choose them, so he asks you for help. 给定一张n个点m条边的图$n\equiv 0(mod\ 3)$,保证存在一个大小为$\frac{2}{3}n$的团,要求输出一个大小为$\frac{n}{3}$的团

输入输出格式

输入格式


In the first line of the standard input two integers, $n$ and $m$ ($3\le n\le 3\ 000$, $\frac{\frac{2}{3}n(\frac{2}{3}n-1)}{2}\leq m\leq \frac{n(n-1)}{2}$), are given,separated by a single space. These denote the number of Byteasar's friends and the number of pairs of his friends who know each other, respectively. Byteasar's friends are numbered from 1 to $n$. Each of the following $m$ lines holds two integers separated by a single space. The numbers in line no. $i+1$ (for $i=1,2,...,m$) are $a_i$ and $b_i$($1\le a_i

输出格式


In the first and only line of the standard output your program should print $\frac{n}{3}$ numbers, separated by single spaces, in increasing order. These number should specify the numbers of Byteasar's friends whom he should invite to the party. As there are multiple solutions, pick one arbitrarily.

输入输出样例

输入样例 #1

6 10
2 5
1 4
1 5
2 4
1 3
4 5
4 6
3 5
3 4
3 6

输出样例 #1

2 4

说明

给定一张n个点m条边的图$n\equiv 0(mod\ 3)$,保证存在一个大小为$\frac{2}{3}n$的团,要求输出一个大小为$\frac{n}{3}$的团 样例图: ![](http://main.edu.pl/images/OI18/impzad1.gif) 由@zhouyonglong提供SPJ