https://code.google.com/codejam/contest/6304486/dashboard
Simple. Nothing to tell.
Catalan Number.
Consider of a way with n upstrokes and m downstrokes.
It's a route from (0, 0) -> (n+m, n-m), totals numbers are (n+m)Cm.
However, the first vote must be A, and afterwards the way cannot
reach the horizontal line. That is, (1, 1) -> (n+m, n-m) where the whole route
is above the horizontal line.
All possible routes number of (1, 1) -> (n+m, n-m) is (n+m-1)C(n-1).
All invalid routes number is (n+m-1)C(m-1) (Reflection,
check here.)
Finally, the result is
((n+m-1)C(n-1)-(n+m-1)C(m-1))/((n+m)Cn) = (n-m)/(n+m).
x*(x+1)/2, where x=min(l, r).