Logic Masters Deutschland e.V.

This puzzle follows in the footsteps of EnTropic Islands by Paletron, as well as my previous puzzle Parity Islands.

Rules:

Normal Sudoku rules apply.

Digits are divided into three 'modular groups' defined by having the same remainder when divided by three (1/4/7, 2/5/8, and 3/6/9). A set of orthogonally connected cells all belonging to the same modular group is a 'modular island'.

A digit in a circle gives the size of the modular island that cell is in. A modular island may have any number of circles within it, and not all possible circles are necessarily given.