A Game With a Sheet of Paper

Yuuko and Nagi like to play the following game: Initially they take a checkered sheet of paper of the size of N x M cells. Then, one cell, let's call this cell (X, Y) is marked. Then, they take the moves alternately. A move consists of making a long horizontal or vertical cut. This cut should coincide with one of the lines that divide the sheet into cells. Then, a part that doesn't contain a mar