Thursday marked the first day of school for New York City’s 1.1 million public school students — and the start of free preschool and free lunch for any pupil who wants, no questions asked.

Until Thursday, the cost of cafeteria lunch had been free or reduced for only the poorest students depending on household income, but families had to fill out paperwork and students who didn’t pay cash were identifiable to peers.

The lunch program is aimed at destigmatizing needy schoolchildren.

The program, which won’t cost the city any more money, is possible because the state changed how it flags families who are eligible for entitlements, boosting the number of eligible students and qualifying the city for a universal free lunch sponsored by the federal government.

“It’s a great thing. It’s something we’re really happy about, and it’s going to allow us to provide free lunch for every child,” said Mayor Bill de Blasio, a Democrat, at a first-day event at a Bronx schoolhouse.

Also Thursday, de Blasio and his wife, Chirlane McCray, kicked off the first municipal-sponsored “3-K” preschool program for 3-year-olds.

“This is an exciting day for everyone, isn’t it? Especially for little ones” McCray said.

The city’s Education Department forecasts the program to cover about 62,000 3-year-olds citywide by the fall of 2021 and costs $12,000 per student.

“One of the greatest things about 3-K — and you’re already starting to see it here — is kids learn to work with each other. They learn to listen. They learn to share. It makes all the difference in the world,” de Blasio said.

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