#P1679D. Toss a Coin to Your Graph...
Toss a Coin to Your Graph...
Description
One day Masha was walking in the park and found a graph under a tree... Surprised? Did you think that this problem would have some logical and reasoned story? No way! So, the problem...
Masha has an oriented graph which $i$-th vertex contains some positive integer $a_i$. Initially Masha can put a coin at some vertex. In one operation she can move a coin placed in some vertex $u$ to any other vertex $v$ such that there is an oriented edge $u \to v$ in the graph. Each time when the coin is placed in some vertex $i$, Masha write down an integer $a_i$ in her notebook (in particular, when Masha initially puts a coin at some vertex, she writes an integer written at this vertex in her notebook). Masha wants to make exactly $k - 1$ operations in such way that the maximum number written in her notebook is as small as possible.
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.
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 $-1$.
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 $-1$.
Samples
6 7 4
1 10 2 3 4 5
1 2
1 3
3 4
4 5
5 6
6 2
2 5
4
6 7 100
1 10 2 3 4 5
1 2
1 3
3 4
4 5
5 6
6 2
2 5
10
2 1 5
1 1
1 2
-1
1 0 1
1000000000
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.