Or you can assume N is less than 2^31, and clear out the top bit in the final answer (because that's the only place the wrong values can come from). Which is admittedly pretty hackish, but…
Edit: The simplest solution is probably just doing (n/2)*(n+1) (assuming n is even; move the division for n odd).
Where S is the sum of the array achieved through iterative addition with every addition mod N and N > 2n.