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}