CF263D.Cycle in Graph

You've got a undirected graph $G$ , consisting of $n$ nodes. We will consider the nodes of the graph indexed by integers from 1 to $n$ . We know that each node of graph $G$ is connected by edges with at least $k$ other nodes of this graph. Your task is to find in the given graph a simple cycle of length of at least $k+1$ .

A simple cycle of length $d$ (d>1) in graph $G$ is a sequence of distinct graph nodes $v_{1},v_{2},...,v_{d}$ such, that nodes $v_{1}$ and $v_{d}$ are connected by an edge of the graph, also for any integer $i$ (1<=i<d) nodes $v_{i}$ and $v_{i+1}$ are connected by an edge of the graph.

The first line contains three integers $n$ , $m$ , $k$ $(3<=n,m<=10^{5}; 2<=k<=n-1)$ — the number of the nodes of the graph, the number of the graph's edges and the lower limit on the degree of the graph node. Next $m$ lines contain pairs of integers. The $i$ -th line contains integers $a_{i}$ , $b_{i}$ $(1<=a_{i},b_{i}<=n; a_{i}≠b_{i})$ — the indexes of the graph nodes that are connected by the $i$ -th edge.

It is guaranteed that the given graph doesn't contain any multiple edges or self-loops. It is guaranteed that each node of the graph is connected by the edges with at least $k$ other nodes of the graph.

In the first line print integer $r$ $(r>=k+1)$ — the length of the found cycle. In the next line print $r$ distinct integers $v_{1},v_{2},...,v_{r}$ $(1<=v_{i}<=n)$ — the found simple cycle.

It is guaranteed that the answer exists. If there are multiple correct answers, you are allowed to print any of them.