Chef and Alien Invasion

Chef has a rectangular field of dimensions $N \times M$ which contains grass all over it. $(0,0)$ is made the bottom left corner of the field. $(N, M)$ is made the top right corner of the field. Aliens aim to destroy the field by sending a cow on the field which will eat all the grass. Chef, in order to protect the field, constructs $K$ rectangular electric fences. An electric fence is represe