If $f^n(a),g^n(a)$ exist and are not equal for some $n$. Further is $f(a) = g(a) =k$ and $\displaystyle\lim_{x \to a} \frac{f(a)g(x) - f(a) - g(a) f(x) + g(a) }{g(x) - f(x)} = 4$, then the value of $k$ is equal to :

Question

( A ) 1
( B ) 4
( C ) 2
( D ) 0