Sherlock Holmes is a renowned detective. His Scotland Yard colleagues often provide him with a set of evidence and ask for his help in solving the mysteries. After many years of practice, Holmes has gained an enormous amount of experience and already knows causes for many common events, which, combined with his extraordinary deductive capabilities, enables him to solve cases in a matter of minutes, from the comfort of his chair.

Holmes' knowledge base can be modeled as a set of implications of the
form (where and represent events), which means that, if
occurred, event must have also occurred (remember that logical
implication is **false** only if is true and is false). Of course,
implications can form chains of reasoning (e.g. ). However,
there will **never** be a **circular** chain of implications (e.g.
).

Holmes is given a set of events
that are known to have occurred. He can then, using his extensive
knowledge and deductive powers, find **all events** that have
**certainly** occurred.

It's important to note that Holmes' knowledge is so mind-bogglingly huge
that he knows **all possible causes of events**. In other words, there
is no implication that is true, but not included in Holmes' knowledge
base.

Many detective agencies would highly appreciate Holmes' one of a kind capabilities, so you were given a task to accomplish with a computer what is out of reach for ordinary mortals. Write a program to find all events that have certainly occurred based on the given implications and evidence collected by your colleague detectives.

#### Input Specification

The first line of input consists of three integers, , the number of different types of events, , the number of implications, and , the number of evidence collected by the detectives.

Each of the lines that follow contains two integers and , describing an implication .

Finally, each of the last lines contain an integer describing an event that must have occurred, based on the evidence collected by detectives.

#### Output Specification

The first and only line of output should contain integers (in any order) representing events that have certainly occurred.

#### 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`

#### Explanation for Sample Output 2

The knowledge base contains implications and . Therefore,
Holmes knows that event can be caused only by events and , but
(without any extra information), he can't be certain **which one** of
those events actually caused . As a result, only event that must have
occurred is the one given in the input.

#### Sample Input 3

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

#### Sample Output 3

`1 2 3 4`

#### Explanation for Sample Output 3

Holmes doesn't know which event from the set is directly
responsible for event . However, as both of those events are caused
**only** by event , Holmes can deduce that event **must have
occurred**. As a consequence, events , and (given by the
detectives) have also occurred.

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