As with Blue Exorcist, the first episode of K didn't quite catch me. However, I have to admit that a scene from the preview at the end of it convinced me to continue immediately.
That girl is a cat, simply called Neko. She belongs to a schoolboy named Yashiro Isana. Yashiro, or Shiro for short, lives on an islet at the boarding school that occupies it. Every student he comes across, often to mooch food off of, likes him. His personality is subdued and kindred. All is normal at the near-future Japanese campus, with its cleaning bots that yell at trash to die, but then Shiro is asked to run some errands in town. There, he's attacked by hoodlums wielding red flames, and saved by a swordsman who battles not with his blade but with arms of midnight-blue energy extended from his own hands.

Can I take a moment to say how adorable this scene is? You should see the Shiro's face in the previous shot! Anyway, once the ship has begun to sail and the two get to a safe rooftop, the swordsman, known as the Black Dog, draws his sword on Shiro. A video a person took one night ended up having recorded him being shot to death. The shooter is a man who claims to be Yashiro Isana, the seventh, colorless king. The shooter looks exactly like Shiro as well. Kuroh has come to the conclusion thus that Shiro is an evil king and, by his master's orders, is determined to execute Shiro. But Shiro doesn't remember committing the crime.
I'm glad that a cat convinced me to continue this series. Of course, the cat alone would have driven me away from it. Combined with beautiful (blushing) boys, supernatural abilities, and mystery, though, Neko heightened my curiosity just to the point that I couldn't just stop watching. Immediately after the first episode, much more humor becomes apparent, starting with Shiro's handling of his execution. Relationships develop and are revealed. The workings of these powers and the concept of the kings are brought out in stages. And the soundtrack is swanky, though at some places incorrectly applied. There's a track played during a helicopter scene that's just so perfect the first time! But I'll let you get to that on your own. I'd rather give you the opening!
Judging by the opening songs of other anime you like, I think this is your thing. ^.^ And as you can see there's a plentiful cast of pretty boys. I'm wondering if you did a double-take, "Was that Axel?" Because that was my first thought upon seeing the Red King. Guess it's inevitable when you've got crimson, spiky hair and flame powers. Another quick note on franchises I've been reminded of. Factions and flame powers? Couldn't help but have Katekyo Hitman Reborn! pop into my head. Not that K should be compared to those two, really. This action-mystery anime that dresses scifi as supernatural should be regarded in its own domain. I'm very sure that you'll enjoy this anime when you put some time aside for it!