The Bad Plus initially established a rep as renegades who’d tackle deconstructed rock/pop tunes, resurrecting them as cutting-edge jazz. Covers of Nirvana, Black Sabbath, and Yes gradually gave way to equally audacious originals, along with a distinctive reading of Stravinsky’s The Rite of Spring. But on this fall’s It’s Hard, the world-trotting, locally bred trio of drummer Dave King, bassist Reid Anderson, and pianist Ethan Iverson returned to their iconoclastic roots with 11 reinvented nuggets by artists ranging from Kraftwerk to TV on the Radio to Barry Manilow. So the band’s annual Christmas week residency at the Dakota should jingle plenty of familiar but wildly twisted bells. Johnny Cash’s “I Walk the Line,” for instance, sports a requisite striding bass via Anderson. The rhythms, however, hiccup, shuffle, slide, slow, and speed up, spewing tangential curiosities along the way. Kraftwerk’s “The Robots” acquires a jaunty spirit and organic core via Anderson and King’s muscular urgency. Prince’s “The Beautiful Ones” retains the lush emotionality of the original while negotiating spiky angularity. Meanwhile, BP’s version of Ornette Coleman’s “Broken Shadows” is strikingly nuanced and introspective.