Let a_n be a sequence recursively defined by: .

So the first 10 elements of a_n are: 1,1,0,3,0,3,5,4,1,9.

Let f(N,M) represent the number of pairs (p,q) such that:

It can be seen that f(10,10)=4 with the pairs (3,3), (5,5), (7,9) and (9,10).

You are also given that f(10⁴,10³)=97158.

Find f(10¹²,10⁶).