John has a box that contains one red ball and one blue ball. Every minute he reaches into the box and randomly takes out a ball from it (without looking). No matter which ball he took out, he puts it back together with another ball of the same color. Thus, after n minutes, the box contains a total of n+2 balls.
The probability that after 2 hours, the box contains exactly 77 blue balls, can be written as ab, where a and b are coprime positive integers. Find a+b.
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