Do you know the chinese remainder theorem? If so let me know, and I will show you a much easier way. I got 76.

If not, you can just multiply and reduce modulo 100 at each stage, and the worst you will ever have to multiply is some 2 digit numbers. It will take a while, but you will get the correct answer. I suggest multiplying in a smart fashion to reduce some of the work like do

2*49=98=-2 (mod 100)

4*48=2*2*48=2*-4=-8 (mod 100)

etc