D. Cycle in Graph
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 ≤ 105; 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 ≤ na 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