If we don't choose $$$i$$$ as a player, then we can take him as an audience member or not take him at all. I claim that if the number of audience members chosen till now $$$ \lt$$$ $$$k$$$ , then we must select $$$i$$$ as an audience member , We can prove this. If we don't select $$$i$$$ as audience, we will need to select some $$$j$$$ ($$$j \gt i$$$ ), strength in that case will include $$$a_j$$$ but not $$$a_i$$$ , but as $$$a_i \ge a_j$$$ , it is always better to select $$$i$$$ .