Given a set of natural numbers {$N_1, ...N_n$} and another natural number $N$, find a closed form solution for the below sum
$M = \sum_{i=1}^n N_i \% N$ <br>
    where $N_i, N, n \in \mathbb N$<br>
    and $N_i \% N$ is the remainder when $N_i$ is divided by $N$
Although trivial, I was able to reduce it to the below form<br><br>
$M = KN + (\sum_{i=1}^n N_i)\%N$<br>
   where $K$ is the quotient when $M$ is divided by N<br><br>
but I am unable to reduce $K$ further into any closed form.<br>
I don't have any formal proof that a closed form can exist, but belief that one could exist has driven be into looking for a solution.
I have been looking up several research papers and questions posted here, but could not get any pointers. Any help is greatly appreciated.