  We give a new proof of Moeckel's result that for any finite index subgroup of
the modular group, almost every real number has its regular continued fraction
approximants equidistributed into the cusps of the subgroup according to the
weighted cusp widths. Our proof uses a skew product over a cross-section for
the geodesic flow on the modular surface. Our techniques show that the same
result holds true for approximants found by Nakada's \alpha-continued
fractions, and also that the analogous result holds for approximants that are
algebraic numbers given by any of Rosen's \lambda-continued fractions, related
to the infinite family of Hecke triangle Fuchsian groups.
