Jerry starts at 0 on the real number line. He tosses a fair coin 8 times. When he gets heads, he moves 1 unit in the positive direction; when he gets tails, he moves 1 unit in the negative direction. The probability that he reaches 4 at some time during this process is \dfrac{a}{b}, where a and b are relatively prime positive integers. What is a+b ? (For example, he succeeds if his sequence of tosses is HTHHHHHH.)
Answer Choices
A. 69
B. 151
C. 257
D. 293
E. 313