Sibasish and Problems

Sibasish has been performing poorly in recent contests. You can check his rating graph here. The graph seems to go down much quicker than it goes up :(. So in an attempt to improve himself, he decides to solve $n$ questions numbered $1$ through $n$. But there are too many questions and so he cannot solve them in a single day. He chooses a positive integer $k ( 4 -> 4 -> 3 -> 3 -> 2 -> 2 -> 1 -> 1