Question 6
Let $A=\{1,2,\ldots,4044\}$. Color 2022 elements of $A$ white and the other 2022 elements black. For $i\in A$, define its weight as the total number of white elements smaller than $i$ and black elements greater than $i$. For each natural number $m$, determine all positive integers $k$ for which a coloring exists with exactly $k$ elements of weight $m$.