VN-TST 2022 Problem 6

Given a set $A=\{1;2;...;4044\}$ . They color $2022$ numbers of them by white and the rest of them by black. With each $i\in A$ , called the important number of $i$ be the number of all white numbers smaller than $i$ and black numbers larger than $i$ . With every natural number $m$ , find all positive integers $k$ that exist a way to color the numbers that can get $k$ important numbers equal to $m$ .