The five students accused of running a cocaine, pot and pill operation out of their Columbia University dorm rooms begged a judge yesterday to spare them from jail and from being forever tarred with felony records.

Prosecutors said they would agree to no-jail deals for four of the five, but demanded that all of the young men plead guilty to felony drug-sale charges.

The most seriously charged of the five — third-year engineering student Harrison David — deserves one year in prison, said prosecutors from the Office of Special Narcotics.

He is accused of selling about $1,300 worth of cocaine to an undercover cop.

David had been selling small quantities of marijuana to help meet tuition costs — and started selling cocaine only at the urging of an undercover drug cop, countered his lawyer, Matthew Myers.

“Marijuana — that’s what they were known for until the undercovers came along,” Myers said.