Let \(S\) be the set of integers between 1 and \(2^{40}\) whose binary expansions have exactly two 1's. If a number is chosen at random from \(S,\) the probability that it is divisible by 9 is \(p/q,\) where \(p\) and \(q\) are relatively prime positive integers. Find \(p+q.\)

(第二十二届AIME2 2004 第10题)