Sum Of Special Evenly-Spaced Elements In Array

Given an array, answer queries (and possibly point updates) that ask for the sum of elements at indices forming an arithmetic progression (a start index and fixed step k) over many operations; constraints are large so you must exploit the evenly‑spaced pattern (e.g., group indices by modulo k, precompute for small k, or use sqrt‑decomposition / indexed structures) to achieve sublinear per‑query time.