Task Ordering with Dependencies and Priorities

You are given n tasks labeled from 1 to n and m dependencies. Each dependency is given as a pair (u, v) indicating that task u must be completed before task v. In addition, each task is assigned a priority. Your goal is to determine an order in which the tasks can be completed such that:

• The ordering is a valid topological order i.e. all dependencies are satisfied.
• If a valid topological order exists, the final ordering is obtained by sorting the tasks from the topological order in descending order of their priorities.

If there exists a cycle in the dependencies, output Not possible. Otherwise, output the list of tasks separated by a space, following the above criteria.

Note: The priorities are given as integers and a higher number indicates a higher priority.

The final answer should be formatted as a space separated string, where task numbers are 1-indexed.

inputFormat

The input is read from stdin and has the following format:

 n m
 p1 p2 ... pn
 u1 v1
 u2 v2
 ...
 um vm

• The first line contains two integers: n (the number of tasks) and m (the number of dependencies).
• The second line contains n integers representing the priorities of the tasks.
• The next m lines each contain two integers u and v, indicating that task u must be completed before task v.

outputFormat

The output is written to stdout. It should be a single line containing either:

• A space separated list of task numbers in the determined order (1-indexed), or
• The string Not possible if no valid ordering exists due to cyclic dependencies.

## sample

4 2
3 2 5 4
1 2
3 4

3 4 1 2