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