Check If Array Pairs Are Divisible by k

Map every value to a non-negative remainder r = ((x % k) + k) % k and count frequencies. A valid pair must use r with (k - r) % k, so for every remainder other than zero and, when k is even, k/2, require count[r] == count[k-r]. Remainder zero items must pair among themselves, so their count is even; the same is true for k/2 because it complements itself. Check that the array length is even first. This argument works even with negative values only if remainders are normalized. Avoid greedily removing pairs from the raw array: the frequency invariant is simpler and safer. Time is O(n + k) and space is O(k), or O(min(n,k)) with a map.