A rectangular floor measures a feet by b feet, where a and b are positive integers with b>a. An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width 1 foot around the painted rectangle and occupies half the area of the entire floor. How many possibilities are there for the ordered pair (a, b) ?

**Answer Choices**

A. 1

B. 2

C. 3

D. 4

E. 5