ILL 1990 Problem 51

Determine for which positive integers $k$ the set $$X = \{1990, 1990 + 1, 1990 + 2, \ldots, 1990 + k\}$$ can be partitioned into two disjoint subsets $A$ and $B$ such that the sum of the elements of $A$ is equal to the sum of the elements of $B.$