Two parabolas have equations y=x^{2}+a x+b and y=x^{2}+c x+d, where a, b, c, and d are integers (not necessarily different), each chosen independently by rolling a fair six-sided die. What is the probability that the parabolas have at least one point in common?
Answer Choices
A. \dfrac{1}{2}
B. \dfrac{25}{36}
C. \dfrac{5}{6}
D. \dfrac{31}{36}
E. 1