Also: If you are using % modulo in your solution, beware of how negative numbers are treated and what value is computed.

Not sure why you're focusing on the number 1023. The parity of the sum of all elements is what is to be determined.

1023 + 1 + 2 = 1026  (even)
-1023 + 1 - 2 = -1024  (even)
1023 + 1 + 3 = 1027  (odd)