We have a simple undirected graph $G$ with $(S+T)$ vertices and $M$ edges. The vertices are numbered $1$ through $(S+T)$, and the edges are numbered $1$ through $M$. Edge $i$ connects Vertices $u_i$ and $v_i$.  
Here, vertex sets $V_1 = \lbrace 1, 2,\dots, S\rbrace$ and $V_2 = \lbrace S+1, S+2, \dots, S+T \rbrace$ are both independent sets.

A cycle of length $4$ is called a 4-cycle.  
If $G$ contains a 4-cycle, choose any of them and print the vertices in the cycle. You may print the vertices in any order.  
If $G$ does not contain a 4-cycle, print `-1`.

What is an independent set? An independent set of a graph $G$ is a set $V'$ of some of the vertices in $G$ such that no two vertices of $V'$ have an edge between them.

Input is given from Standard Input in the following format:

```
$S$ $T$ $M$
$u_1$ $v_1$
$u_2$ $v_2$
$\vdots$
$u_M$ $v_M$
```

If $G$ contains a 4-cycle, choose any of them, and print the indices of the four distinct vertices in the cycle. (The order of the vertices does not matter.)  
If $G$ does not contain a 4-cycle, print `-1`.

-   $2 \leq S \leq 3 \times 10^5$
-   $2 \leq T \leq 3000$
-   $4 \leq M \leq \min(S \times T,3 \times 10^5)$
-   $1 \leq u_i \leq S$
-   $S + 1 \leq v_i \leq S + T$
-   If $i \neq j$, then $(u_i, v_i) \neq (u_j, v_j)$.
-   All values in input are integers.

1 2 4 5

There are edges between Vertices 1 and 4, 4 and 2, 2 and 5, and 5 and 1, so Vertices 1, 2, 4, and 5 form a 4-cycle. Thus, 1, 2, 4, and 5 should be printed.
The vertices may be printed in any order. Besides the Sample Output, 2 5 1 4 is also considered correct, for example.

-1

Some inputs may give G without a 4-cycle.