NEW YORK (AP) — Officials getting ready for a massive expansion in the city's prekindergarten enrollment were spending the last day before school starts finishing inspections of every single facility. Officials said the vast majority of the 1,700 sites will open on the first day of school Thursday and are poised to serve an unprecedented jump from 20,000 to 53,000 students in a single year. The expansion — the centerpiece of de Blasio's first year in office — has been closely watched nationally and drew some surprising criticism last week from the city comptroller, who expressed safety concerns about the program. By law, every pre-K staffer must clear a background check, though a teacher whose approval is pending is permitted to deal with children if a cleared supervisor is present. Comptroller Scott Stringer, normally a reliable de Blasio ally, criticized City Hall last week for being sluggish in sending contracts with pre-K vendors to his office for review.