One more to try: this one doesn't require the values to be integers, but it's a bit longer and still requires the CSE:
=INDEX($AT$1:$BE$1,SMALL(IF($AT2:$BE2=LARGE($AT2:$BE2,COLUMNS($BF2:BF2)),COLUMN($AT2:$BE2)-COLUMN($AT2)+1),COLUMNS($AT2:AT2)-COUNTIF($AT2:$BE2,">"&LARGE($AT2:$BE2,COLUMNS($BF2:BF2)))))