A 62-year-old woman is referred to a neurologist for a 2-year history of progressive weakness in her lower extremities resulting in several falls, difficulty rising from a chair, and burning in her hands and feet. The patient has a history of migraine headaches in her youth but has not had any migraines in many years. She is a retired school teacher with no unusual exposures. Her physical exam is significant for weakness in her lower extremities, especially the hip flexors, ankle and foot muscles. She also has weakness of her finger extensors. Her sensory exam shows loss of sensation in a stocking and glove distribution bilaterally. The deep tendon reflexes are absent. The rest of the neurologic exam is normal. What is the most likely diagnosis?

A. arsenic polyneuropathy
B. chronic inflammatory demyelinating polyneuropathy
C. diabetic polyneuropathy
D. inflammatory myopathy
E. transverse myelitis