T661249 [SWERC 2020] Restaurants

:::align{center}  ::: Everybody is very happy to go back outside and to restaurants in Paris. However, for a while yet the restaurants have a very limited number of seats. We want to ensure that both restaurants can receive as many people as possible, and that customers go in their preferred seats. We have $N$ customers, numbered from $1$ to $N$, and $M$ restaurants, numbered from $1$ to $M$. Each customer makes reservation in a subset of the restaurants, and give their list of reservations ordered by preference. Each restaurant ranks the reservations it received by some order of preference -- for instance, the restaurant might wish customers who have signed up first to be ranked higher. Each restaurant $i$ also has a capacity $c_i$, i.e. the maximal number of customers it can support. Your task is to find an allocation of *some* of the customers in restaurants such that the following conditions are fulfilled: 1. No restaurant places more customers than their capacity. 2. Each customer is given a table in at most one restaurant. 3. There is no restaurant $r$ and customer $c$ having made a reservation for $r$, such that: - $c$ has not been given a table or prefers $r$ to the restaurant he was given a table in, and - $r$ has some seats left or $r$ is full but prefers $c$ to at least one of the customers assigned to it. Other remarks to note: - Every customer has made at least one reservation. - Restaurants only rank the customers having expressed a reservation for them. It is possible that a restaurant has no customers wishing to make a reservation.

The first line contains $N$ and $M$. The $M$ following lines describe capacities with the $i$-th line containing an integer $c_i$, the capacity of restaurant $i$. $N$ lines follow. The $i$-th line describes the list of reservations for customer $i$, sorted by preferences: the line contains a list of distinct space-separated integers (between 1 and $M$), from most to least preferred. $M$ lines follow. The $i$-th line describes the sorted preferences of restaurant $i$. This line contains either the number 0 when no customer made a reservation to restaurant $i$ or it contains a list of space-separated distinct integers, the list of customers who made a reservation to restaurant $i$ ordered from most to least preferred by the restaurant. **Limits** - $1\leq N \leq 50\,000$ - $1\leq M \leq 10\,000$ - total number of reservation options is at most $1\,000\,000$. - $1\leq c_i \leq N$

The output described the set of customers which have a table in one possible allocation (according to the rules above). The set is given with one customer per line, sorted ascending by id.