<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _list_existing(filesystem, glob, paths):
 """ Get all the paths that do in fact exist. Returns a set of all existing paths. Takes a luigi.target.FileSystem object, a str which represents a glob and a list of strings representing paths. """

    globs = _constrain_glob(glob, paths)
    time_start = time.time()
    listing = []
    for g in sorted(globs):
        logger.debug('Listing %s', g)
        if filesystem.exists(g):
            listing.extend(filesystem.listdir(g))
    logger.debug('%d %s listings took %f s to return %d items',
                 len(globs), filesystem.__class__.__name__, time.time() - time_start, len(listing))
    return set(listing)