Problem Statement

You are given an undirected graph with $N$ vertices and $M$ edges, containing no self-loops or multiple edges.
The $ i (1 \le i \le M)$-th edge connects vertex $u_i$ and vertex $v_i$.
When moving from vertex $S$ to vertex $G$ while traversing edges exactly $P$ times in total, find all vertices that may be passed through (including $S, G$).

The writer has confirmed that this problem can get AC using PyPy3, but it has not been confirmed whether AC is possible with Python3.
Please be very careful when submitting in Python.

Input

$N\ M\ P$
$S\ G$
$u_1\ v_1$
$u_2\ v_2$
$\vdots$
$u_M\ v_M$

All inputs are integers.
$2 \le N \le 10^5$
$1 \le M \le min(10^5,N \times (N-1)/2)$
$1 \le P \le 10^9$
$1 \le S, G \le N$
$S \neq G$
$1 \le u_i , v_i \le N$
$ u_i \neq v_i $
When $ i \neq j $, $ (u_i, v_i) \neq (u_j, v_j) $ and $ (u_i, v_i) \neq (v_j, u_j) $

Output

First, output the number $K$ of vertices that may be passed through, and then, on the following $K$ lines, output the vertices that may be passed through in ascending order.
However, if no movement satisfying the condition is possible, output $-1$.
Print a newline at the end.

Sample

Sample 1

Input

6 5 3
1 4
1 2
1 3
1 4
2 5
3 6

Output

4
1
2
3
4

There are $(1→2→1→4),(1→3→1→4),(1→4→1→4)$, a total of 3 ways to go from point 1 to point 4 while traversing edges 3 times.

4 3 4
1 4
1 2
2 3
3 4

-1

10 9 5
1 10
7 2
4 9
5 3
1 9
2 9
8 7
8 5
6 4
10 2

6
1
2
4
7
9
10