260.The Ballot Problem

Candidates $A$ and $B$ receive $n$ and $m$ votes respectively, with $n > m$. The $n + m$ ballots are shuffled and drawn one-by-one, keeping a running tally. The probability that $A$ is never behind in the count (ties allowed, excluding the initial $0$–$0$ state) is a function $Q(n, m)$. Find $Q(100, 80)$.