We report on νe and ν̅ e appearance in νμ and ν̅ μ beams using the full MINOS data sample. The comparison of these νe and ν̅ e appearance data at a 735 km baseline with θ13 measurements by reactor experiments probes δ, the θ23 octant degeneracy, and the mass hierarchy. This analysis is the first use of this technique and includes the first accelerator long-baseline search for ν̅ μ→ν̅ e. Our data disfavor 31% (5%) of the three-parameter space defined by δ, the octant of the θ23, and the mass hierarchy at the 68% (90%) C.L. We measure a value of 2sin⁡2(2θ13)sin⁡2(θ23) that is consistent with reactor experiments.