Passing On a Good Deed

Sangwon Lee, who has no problems with his character, often shares good deeds about the people around him. People's relationships are tangled, so when you tell someone a good deed about a person, it travels around and eventually reaches that person.

Relationships and good deeds are defined as follows.

• A relationship is one-way. That is, even if $A \rightarrow B$ holds, $B \rightarrow A$ may not hold.
• When a relationship $A \rightarrow B$ is given, $B$ is one of the people close to $A$.
• Each person may hear a good deed several times. Whenever person $A$ hears a good deed, $A$ picks one of the people close to them and passes it on.

A good deed only matters once it reaches the person it is about. Suppose a good deed starts from $A$ and reaches a third person $C$. If it can then reach the subject through $C$, then $A$ is called a 'direct good deed spreader' and $C$ is called an 'indirect good deed spreader'. The subject can also create indirect spreaders, and the subject can become an indirect spreader too. A direct spreader cannot become an indirect spreader.

In the relationships shown above, if the subject is person 3 and the direct spreader is person 1, then the indirect spreader is {2}, which is 1 person.

Sangwon wants to spread a good deed about the subject $K$. He does not want to tell many people, so he will pass it to only one direct spreader. He chooses a direct spreader $X$ ($X \neq K$) and passes the good deed to them. What is the maximum number of indirect spreaders that can arise?

The first line contains $N$ ($1 \le N \le 10,000$) and $M$ ($0 \le M \le 100,000$). These are the number of people and the number of relationships, respectively.

From the second line through line $M+1$, the $M$ relationships are given. Each line contains two integers $u$ and $v$ ($1 \le u, v \le N$, $u \ne v$) separated by a space. This means a relationship $u \rightarrow v$. No relationship is given twice.

The last line contains an integer $K$ ($1 \le K \le N$). This is the subject of the good deed.

On the first line, print $X$, the direct spreader defined in the problem, and the number of indirect spreaders caused by $X$, separated by a space. If several values of $X$ give the same maximum, print the smallest one. If no indirect spreader can arise, print 0 on the first line.

If the good deed is passed to person 1, the spreading path is 1→2→3→1→2→4→5→6→7→8→7. The indirect spreaders are {2, 3, 4, 5, 6, 7, 8}, which is 7 people.