Problem Description

Translated from COCI 2010.03.20 T5 "HOLMES"

There are $D$ events, numbered from $1$ to $D$.

Sherlock Holmes has $M$ inferences of the form $A \rightarrow B$, indicating that "if event $A$ occurs, then event $B$ will definitely occur." Note that this does not imply "if $A$ does not occur, then $B$ will definitely not occur."

These $M$ inferences can form chain structures, such as $A \rightarrow B \rightarrow C$, but they will never form loops, like $A \rightarrow B \rightarrow C \rightarrow \dots \rightarrow A$.

Given that events $S_1 \ldots S_N$ will occur, determine which events will definitely occur.

Update: The original problem statement was unclear (or my Chinese is too poor), so I added a sentence to explain Sample 1. For an event $X$, if there are inferences $Y_1 \rightarrow X$, $Y_2 \rightarrow X$, then "event $X$ will definitely occur" if and only if "event $Y_1$ will definitely occur" or "event $Y_2$ will definitely occur"…

Input Format

The first line contains three integers: $D$, $M$, and $N$.
The next $M$ lines each contain two integers, representing an inference $A_i, B_i$.
The next $N$ lines each contain one integer $S_i$.

Output Format

Output a single line containing several integers, representing the events that will definitely occur.
Please output them in increasing order of their numbers, as the problem setter is too lazy to write a special judge.

Sample Input and Output

Sample Input #1

3 2 1
1 2
2 3
2

Sample Output #1

1 2 3

Sample Input #2

3 2 1
1 3
2 3
3

Sample Output #2

3

Sample Input #3

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

Sample Output #3

1 2 3 4

Sample Input #4

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

Sample Output #4

3 4

Notes

Sample Explanation #2

Knowing only that event 3 occurs, we cannot deduce whether it was caused by event 1 or event 2.

Sample Explanation #3

Event 4 occurs, so at least one of events 2 and 3 must occur.
Either way, their condition is that event 1 must occur.
Since event 1 must occur, events 2 and 3 must also occur.

Sample Explanation #4

Event 3 occurs, so at least one of events 1 and 2 must occur.
If either event 1 or event 2 occurs, event 4 will definitely occur.

Data Range and Hints

$1 \le D \le 1000$, $1 \le M \le 10^5$, $1 \le N$, $X_i$, $A_i$, $B_i \le D$.

见题面 Input 部分

见题面 Output 部分