In normal Nim game, the player taking the last object wins.
And terminal position here is always a P -position.
Now, I have a question where you are given the terminal P and N positions unlike the only terminal condition in normal Nim.
Is this a variation of Nim? If yes, how to analyze it, how should I go about assigning grundy numbers?

Formally:
I have n heaps with represented by a set S={a₁,a₂,a₃, .... a_n}.
And, I have a set T which gives terminal positions and tell whether it is a P-position or N-position.
One element of the set can be {{k₁,k₂,k₃, .... k_n},P}
where,
k₁<=a₁
k₂<=a₂
k₃<=a₃
.
.
k_n<=a_n

It means the set {k₁,k₂,k₃, .... k_n} is a terminal position.
And, the second parameter denotes either 'P' or 'N' as P-position or N-position.

Can this be made equivalent to Nim?
How to analyze this?