MathNet 2021 — Part 07 Question 12

For every nonnegative real number $x$, let $\lfloor x\rfloor$ be its integer part, the greatest integer less than or equal to $x$, and let $\{x\}=x-\lfloor x\rfloor$ be its fractional part.

Let $p$ be a positive, noninteger real solution of $\{z\lfloor z\rfloor\}=2021\{z\}$. What is the second-smallest possible value of $\lfloor p\rfloor$?