Ive need this in some problems, but I can't figure out how to count it. I will be glad to useful ideas.

How many different arrays of length n are there of non-negative integers with sum of k; n <= 10^5, k <= 10^9

I'm glad I became an expert, but i dont understand why my rating increased last div3 round. I had 1598 rating and finished ~600th. I was sure my rating would fall. Post about rating system says that my rating will increase if I place higher than expected. Wasn't my expected place ~1? (it was div3 (only <1600))

Maybe i dont understand math part of post, so can somebody tell my how rating changes actually works, please?