6. For a one-dimensional system, a transformation of variables, (q,p) ? (Q, P), is performed such that
$Q = q^k p^l$;
$P = q^m p^n$;
where k, l, m and n are real constants.
(a) How are k, l, m, n to be chosen in order to make the transformation canonical?
(b) Which (canonical) transformation comes out in particular for m = 0?
(c) Determine the type-1 generating function F?(q, Q) to produce such canonical transformation in (a).