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.

Input

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.

Output

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.