Pink’s new album, “Beautiful Trauma,” hits stores Friday, but there’s no sign of the songs from a writing session she had with Billy Joel on it.

“The problem is he’s too good for me,” she told the Los Angeles Times. “I clammed up. But we’re gonna keep trying. He goes, ‘Do me a favor: Go home, pick out the best poem you’ve ever written and send it to me, and I’ll make you a song.’ I got home and was like, ‘All my poems are the worst pieces of trash I’ve ever seen in my life.’ ”

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Joel told Newsday that he had enjoyed working with the “Get the Party Started” singer, but didn’t know what would happen with the songs they wrote together. The five-time Grammy winner released his last album of pop music, “The River of Dreams,” in 1993 and has only released a handful of pop songs since then, though he says he continues to write music of all types.

Pink, in her L.A. Times interview, explained how she got Joel, who has rarely written songs with anyone, to work with her.

“I’ve never stopped asking,” the three-time Grammy winner said. “He always says no — he’s kind, but he’s firm. But then we ran into him in the Bahamas at a piano bar. I bought a very good bottle of wine and sent him a glass. He came over and I said, ‘You gonna write that song with me?’ He said, ‘OK, I’ll try it.’ So several months ago I flew to Palm Beach with my brand-new baby and we tried to write a song.”

It didn’t quite work because Pink, whose first concert was Joel’s “The Bridge” tour, was a little intimidated.

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“Billy Joel is in my opinion one of the best songwriters that’s ever lived,” she said. “He paints a picture with words unlike any other. I walked down the aisle to ‘She’s Always a Woman.’ I grew up listening to him with my dad.”