Two weeks ago, ABC late-night host Jimmy Kimmel and musician Kanye West got into a public brawl on TV and Twitter. Kimmel jokingly called it his "first rap feud," and swore it wasn't just another one of his publicity stunts.

On Wednesday night, just to prove it wasn't a ratings ploy, Kimmel had Kanye on his show to straighten things out. It's sort of like watching a therapy session, where the TV audience is the psychologist. When West came out, he and Kimmel didn't just shake hands. They hugged, albeit somewhat awkwardly.

Then Kimmel explained his side of the feud.

He played the clip that so offended Kanye — two children re-enacting a particularly self-aggrandizing portion of an interview West did with BBC Radio — then confessed that he didn't watch the whole interview before doing the sketch. "I figured," Kanye replied.

Kimmel said that West and much of the TV/internet audience may not be aware of it, but he's done this child re-enactment thing with Lady Gaga and other celebrities. "The main reason I did that is because I like to see kids curse," he added, getting the first laugh of the night from his guest. Then he and Kanye swore once more that this isn't one big publicity stunt. "I don't do publicity stunts, period," Kanye added. Because of course he said that.

In Part 2 of the interview, Kanye gave us his side of the story. He took Kimmel's skit so personally, he explained, because he knows Kimmel, and because he's built up a lot of steam from years of being disrespected by journalists and paparazzi he doesn't know. "We kind of just took it back to high school for a little bit," West explained, summing up their whole feud. Another highlight: Kimmel told West: "A lot of people think you're a jerk." Watch Kanye's expression:

The rest of the interview is below. It's largely a monologue by Kanye, about Kanye. And since West is a pretty entertaining monologist, there are some real gems for those with 16 minutes to spare: