Three balls are randomly and independently tossed into bins numbered with the positive integers so that for each ball, the probability it is tossed into bin i is 2^{-i} for i=1,2,3, \ldots. More than one ball is allowed in each bin. The probability that the balls end up evenly spaced in distinct bins is \dfrac{p}{q}, where p and q are relatively prime positive integers. (For example, the balls are evenly spaced if they are tossed into bins 3,17 , and 10.) What is p+q ?
Answer Choices
A. 55
B. 56
C. 57
D. 58
E. 59