I need to implement data structure that can answer for O(logn) to these queries:

Given sequence f(n), f(-2) = f(-1) = 1, f(n) = (a(n) * f(n-1) + b(n) * f(n-2)) mod M, queries:

1. replace pair (a(i), b(i)) with (a, b);
2. evaluate f(i) for given i.

I was thinking about Fenwick tree and fast matrix multiplication for finding i-th element of reccurent sequence, but I’m not sure if it’s a good approach.