Toss a Coin to Your Graph...

Description:

Input:

The first line contains three integers $$$n$$$, $$$m$$$ and $$$k$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$0 \le m \le 2 \cdot 10^5$$$, $$$1 \le k \le 10^{18}$$$) — the number of vertices and edges in the graph, and the number of operation that Masha should make.

The second line contains $$$n$$$ integers $$$a_i$$$ ($$$1 \le a_i \le 10^9$$$) — the numbers written in graph vertices.

Each of the following $$$m$$$ lines contains two integers $$$u$$$ and $$$v$$$ ($$$1 \le u \ne v \le n$$$) — it means that there is an edge $$$u \to v$$$ in the graph.

It's guaranteed that graph doesn't contain loops and multi-edges.

Output:

Print one integer — the minimum value of the maximum number that Masha wrote in her notebook during optimal coin movements.

If Masha won't be able to perform $$$k - 1$$$ operations, print $$$-1$$$.

Sample Input:

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

Sample Output:

4

Sample Input:

6 7 100
1 10 2 3 4 5
1 2
1 3
3 4
4 5
5 6
6 2
2 5

Sample Output:

10

Sample Input:

2 1 5
1 1
1 2

Sample Output:

-1

Sample Input:

1 0 1
1000000000

Sample Output:

1000000000

Note:

Graph described in the first and the second examples is illustrated below.

In the first example Masha can initially put a coin at vertex $$$1$$$. After that she can perform three operations: $$$1 \to 3$$$, $$$3 \to 4$$$ and $$$4 \to 5$$$. Integers $$$1, 2, 3$$$ and $$$4$$$ will be written in the notepad.

In the second example Masha can initially put a coin at vertex $$$2$$$. After that she can perform $$$99$$$ operations: $$$2 \to 5$$$, $$$5 \to 6$$$, $$$6 \to 2$$$, $$$2 \to 5$$$, and so on. Integers $$$10, 4, 5, 10, 4, 5, \ldots, 10, 4, 5, 10$$$ will be written in the notepad.

In the third example Masha won't be able to perform $$$4$$$ operations.