A Princeton slot machine has 100 pictures, each equally likely to occur. One is a picture of a tiger. Alice and Bob independently use the slot machine, and each repeatedly makes independent plays. Alice keeps playing until she sees a tiger, at which point she stops. Similarly, Bob keeps playing until he sees a tiger. Given that Bob played twice longer than Alice, let the expected number of plays for Alice be \frac{a}{b} with a, b relatively prime positive integers. Find the remainder when a+b is divided by 1000.