Integers a, b, c, and d, not necessarily distinct, are chosen independently and at random from 0 to 2007 , inclusive. What is the probability that a d-b c is even?
Answer Choices
A. \dfrac{3}{8}
B. \dfrac{7}{16}
C. \dfrac{1}{2}
D. \dfrac{9}{16}
E. \dfrac{5}{8}