Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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

D. Cycle in Graph

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou'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.

Examples

Input

3 3 2

1 2

2 3

3 1

Output

3

1 2 3

Input

4 6 3

4 3

1 2

1 3

1 4

2 3

2 4

Output

4

3 4 1 2

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/27/2017 06:22:32 (c3).

Desktop version, switch to mobile version.
User lists

Name |
---|