Let S be the square one of whose diagonals has endpoints (0.1,0.7) and (-0.1,-0.7). A point v=(x, y) is chosen uniformly at random over all pairs of real numbers x and y such that 0 \leq x \leq 2012 and 0 \leq y \leq 2012. Let T(v) be a translated copy of S centered at v. What is the probability that the square region determined by T(v) contains exactly two points with integer coordinates in its interior?
Answer Choices
A. 0.125
B. 0.14
C. 0.16
D. 0.25
E. 0.32