MathNet 2014 Question 80

There were two parallel railways, on the first of which are $n$ stations and on the other are $m$ stations. A company constructed a new station between the railways and connected by railways the new station with the old ones. From an economical point of view, the company decided to close some railways between stations to have only $n + m$ railways. How many ways can it be arranged so that one could make a journey from any station to any other station?
(proposed by B. Horoldagwa)