We have 2022 1s written on a board in a line. We randomly choose a strictly increasing sequence from 1,2,...,2022 such that the last term is 2022. If the chosen sequence is a1,a2,...,ak (k is not fixed), then at the ith step, we choose the first ai numbers on the line and change the 1s to 0s and 0s to 1s. After k steps are over, we calculate the sum of the numbers on the board, say S. The expected value of S is ba where a,b are relatively prime positive integers. Find a+b. probabilityexpected valuenumber theoryrelatively prime