Most General form of Canonical Transformation

• A
kolawoletech
How do I go about finding the most general form of the canonical transformation of the form
Q = f(q) + g(p)
P = c[f(q) + h(p)]
where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and conjugate momentum in the new and old system

$$\{Q,Q\}=\{P,P \}=0, \quad \{Q,P \}=1$$