XOR After Range Multiplication Queries II

Given nums and queries [l,r,k,v] that multiply every element at indices l, l+k, l+2k,... ≤ r by v (mod 1e9+7), return the bitwise XOR of the final array. With n,q up to 1e5, the core challenge is to apply multiplicative updates to arithmetic subsequences (indices sharing the same residue mod k) efficiently instead of updating each element per query.