It is a really cool math problem, and we should be using math to solve it! This problem took me 30 minutes to solve without programming and so I'm only a few minutes off Fortran. (I scale well too since I can now do it in constant time - fine log time if we count reading the input.)

A minor nit to pick: the 1,448,575,636 number is not the number of buyouts. (It looks like the number of nodes in the evaluation graph.)

Spoiler: the answer is 111110110111_2. (edit: had the wrong answer)