407967: GYM102953 4 School Contact Tracing

You go to a school with $$$n$$$ students, all of which can be identified by a unique student ID from 1 to $$$n$$$, inclusive. The school has $$$m$$$ classes, each consisting of $$$k$$$ students.

Unfortunately, $$$c$$$ students just tested positive for COVID-19, and the school is figuring out which other students need to go into quarantine due to the $$$c$$$ students testing positive.

Since the school is being very cautious, they decide to have any students in at least one class with the $$$c$$$ students quarantine, but the school decides to extend the rule and have any students in a class with a quarantined student quarantine as well. This continues in a "chain reaction" process, until there are no more additional students that have to quarantine.

Given the $$$c$$$ students that just tested positive, figure out the ID's of any additional students that have to quarantine (not including the original $$$c$$$ students).

The first line of input consists of three space-separated integers $$$n$$$ $$$(1 <= n <= 10^5)$$$, $$$m$$$ $$$(1 <= m <= 10^5)$$$, and $$$k$$$ $$$(1 <= k <= 10^5)$$$, $$$m * k <= 10^5$$$: the number of students in the school, the number of classes in the school, and the number of students in each class, respectively.

The next $$$m$$$ lines each contain $$$k$$$ distinct space-separated integers: the student ID's of each student in each class.

The next line contains a single positive integer $$$c$$$ $$$(1 <= c <= n)$$$: the number of students that recently tested positive for COVID-19.

The next line contains $$$c$$$ distinct space-separated positive integers: the student ID's of the students that recently tested positive.

Output a single positive integer $$$q$$$: the number of additional students that have to quarantine.

Then, output a single line consisting of $$$q$$$ space-separated integers in ascending order: the number of students that will have to quarantine (not including the students that already tested positive).

Subtask 1 (14 points): $$$(1 <= n, m, k, m*k <= 1000)$$$

Subtask 2 (9 points): no additional constraints

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