Cycle in Graph

Description:

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 ≤ 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 v₁, v₂, ..., 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.

Sample Input:

3 3 2
1 2
2 3
3 1

Sample Output:

3
1 2 3 

Sample Input:

4 6 3
4 3
1 2
1 3
1 4
2 3
2 4

Sample Output:

4
3 4 1 2