2025 AMC 12B Problem 23

Let S be the set of all integers z \gt 1 such that for all pairs of nonnegative integers (x, y) with x \lt y \lt z, the remainder when 2025x is divided by z is less than the remainder when 2025y is divided by z. What is the sum of the elements of S?

\textbf{(A)} 3041 \qquad \textbf{(B)} 3542 \qquad \textbf{(C)} 3750 \qquad \textbf{(D)} 4044 \qquad \textbf{(E)} 4319

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.