The new PUMaC tournament hosts 2020 students, numbered by the following set of labels 1,2, \ldots, 2020. The students are initially divided up into 20 groups of 101, with each division into groups equally likely. In each of the groups, the contestant with the lowest label wins, and the winners advance to the second round. Out of these 20 students, we chose the champion uniformly at random. If the expected value of champion’s number can be written as \frac{a}{b}, where a, b are relatively prime integers, determine a+b.