Probability of having the same birthday

I think I know how to do the problem, but I run into the problem that in Excel, the numbers that need to be calculated are too large and thus I cannot get an answer. If you can solve this without having this problem, I would love to know how you did it...

Find the smallest number of people in a room so that the probability that at least two people in the room were both born on April 1 exceeds 1/2. (Assume all birthdays are equally likely and that the year has 366 days.)