According to The Beatles Bible, John Lennon and Paul McCartney were walking in London one day when Mick Jagger and Keith Richards happened to pass them in a taxi. The rock rebels called over from the vehicle, and McCartney and Lennon hopped in. According to Barry Miles’ biography of Lennon, “Many Years From Now,” the musician explained what happened next: “There were the four of us sitting in a taxi and I think Mick said, ‘Hey, we’re recording. Got any songs?'”

UDiscover Music tells a slightly different version of this contested tale. The outlet reports that Andrew Loog Oldham, the Rolling Stones’ manager, happened upon The Beatles duo while taking a break from the Stones’ recording session at London’s Studio 51. However it happened, though, the result was the same: The Stones needed a cover song, as they had reportedly scrapped a release of The Coasters’ “Poison Ivy” — their intended second single — after conflicts with the producer. And lucky for them, The Beatles quickly provided.

Per UDiscover Music, the bands completed the piece together in the studio and adapted it to their respective styles, going on to release it just weeks apart. This was just one example of the talented songwriting team of McCartney and Lennon giving songs to other big names. For instance, they also wrote Gerry and The Pacemakers’ “Do You Want To Know A Secret,” per Ultimate Classic Rock.