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: \begin{itemize} \item $c$ has not been given a table or prefers $r$ to the restaurant he was given a table in, and \item $r$ has some seats left or $r$ is full but prefers $c$ to at least one of the customers assigned to it. \end{itemize} Other remarks to note: \begin{itemize} \item Every customer has made at least one reservation. \item 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. \end{itemize} \InputFile The first line contains $n~(1 \le n \le 50000)$ and $m~(1 \le m \le 10000)$. The $m$ following lines describe capacities with the $i$-th line containing an integer $c_i~(1 \le c_i \le n)$, 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 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 distinct integers, the list of customers who made a reservation to restaurant $i$ ordered from most to least preferred by the restaurant. The total number of reservation options is at most $10^6$. \OutputFile 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 $id$.