## Task B-1.2.

Given the expression $\quad|x-1|+|x-2|+|x-3|+\ldots+|x-2019|+|x-2020|$.

Determine the largest interval of real numbers $[a, b]$ on which the given expression has a constant value $k$ for all $x \in[a, b]$. What is the value of the constant $k$?