Paper Folding

There is a piece of paper P in the shape of an N-sided convex polygon on a 2D coordinate plane. The vertices of this paper are given as (A1,B1),(A2,B2),…,(AN,BN).

From the interior of this paper P, an M-sided convex polygonal region Q is cut out. The vertices of the region Q to be cut out are given as (C1,D1),(C2,D2),…,(CM,DM), and Q along with its boundary is completely contained within the interior of P.