Authorities across the U.S. Northeast cautioned residents Tuesday to stay off the roads, and thousands of school districts have canceled classes in the region as a raging winter storm has begun to batter Philadelphia, New York City, Boston, and elsewhere. Gov. Andrew Cuomo declared a state of emergency for each of New York’s 62 counties, and he demanded that all nonessential state employees stay home rather than commute to work. More than 5,000 flights have so far been canceled, including more than 2,800 in the New York City area alone. The storm, according to the National Weather Service, will drop between 12 inches and 18 inches of snow across the region. The New Jersey Shore is at risk of strong winds between 50 to 55 mph and a storm surge.