Compute the Fibonomial Coefficient Background
The Fibonacci sequence is defined as
$$f(1) = 1 \\ f(2) = 1 \\ f(n) = f(n-1) + f(n-2)$$
The Fibonorial, similar to the factorial, is the product of the first \$n\$ Fibonacci numbers.
$$g(n) = f(1) \times f(2) \times ... \times f(n-1) \times f(n)$$
The Fibonomial coefficient, similar to the binomial coefficient is defined as
$$\begin{align}a(n, 0) &amp; = 1 \\
a(n, k) &amp; = \frac {g(n)} {g(n-k) \times g(k)} \\
&amp; = \frac {f(n) \times f(n-1) \times ... \times f(n-k+1)} {f(1) \times f(2) \times ... \times f(k)}
\end{align}$$
Task
Your goal is to create a function or program to compute the Fibonomial coefficient given two non-negative integers \$n\$ and \$k\$ with \$l \le n\$.
Test Cases
a(0, 0) = 1
a(1, 1) = 1
a(2, 0) = 1
a(3, 2) = 2
a(8, 3) = 1092
a(11, 5) = 1514513
a(22, 7) = 7158243695757340957617
a(25, 3) = 49845401197200
a(50, 2) = 97905340104793732225
a(100, 1) = 354224848179261915075

Rules

This is code-golf so the shortest code wins.
Builtins are allowed.

Related

A000045 - Challenge - Fibonacci Sequence
A003266 - Challenge - Fibonorial
A010048 - Fibonomial coefficient
Python 67 bytes
f=lambda n,a=1,b=1:n&lt;1or a*f(n-1,b,a+b)
lambda n,k:f(n)/f(k)/f(n-k)

Call using a(n,k). Uses @Dennis fibonorial answer (is that allowed?), and a straightforward implementation of the question otherwise.