Math Help - Markov Chain Problem

1. Markov Chain Problem

Consider two dogs (Spot and Lassie) su ffering from a total number of $m$ fleas. Spot initially has $b$ fleas and Lassie initially has the remaining $m - b.$ The fleas have
agreed on the following immigration policy: at times $n = 1,2....$ a flea is selected uniformly at random from the total population and that
flea will jump from one dog to the other.

Describe the flea population on Spot as a Markov chain and find the stationary distribution $\pi$ of the chain.

2. I have tried and tried to work this out. I feel like crying.

I know its a birth death process, and based on Ehrenfest's diffusion model, but I have been trying to work this problem out for a week now and have not solved anything. Can anyone please help