At the start of the PUMaC opening ceremony in McCosh auditorium, the speaker counts 90 people in the audience. Every minute afterwards, either one person enters the auditorium (due to waking up late) or leaves (in order to take a dreadful math contest). The speaker observes that in this time, exactly 100 people enter the auditorium, 100 leave, and 100 was the largest audience size he saw. Find the largest integer m such that 2^{m} divides the number of different possible sequences of entries and exits given the above information.