2022 SSMO Team Round Problems/Problem 8
Problem
A frog is at 
on a number line and wants to go to 
. On each turn, if the frog is at 
, the frog hops to one of the numbers from to , inclusive, with equal probability (staying in place counts as a hop). It is then teleported to the largest multiple of 
that is less than or equal to the frog's position. The expected number of hops it takes for the frog to reach can be expressed as 
, where 
and are relatively prime positive integers. Find 
.
