If you consider prefix sums of size 1, 2, 3... N, there are N different prefix sums. If all of the prefix sums are different mod N, then you know one of them is divisible by N and the solution is that entire prefix sum(because there are N residues mod N and N prefix sums). Otherwise, if the prefix sums are not all different mod N, then that means that two of them are congruent, so the set you want is just the larger prefix sum minus the smaller one of the same residue mod N.