I was really looking forward this original anime but the first episode was a big disappointment. The start reminded me a bit of Shin Sekai Yori. In both anime we are thrown in future and the first episode leaves with more questions than answers. But while Shin Sekai Yori managed to make some things clear in order to make audience to understand basics of what's going on, K left me way too confused. It seems like the story is taking place sometime in the future with advanced technology. Trains under the bridges looks rather interesting, though. Another confusing thing is characters. It turns out that all these cool characters (one of them looks really like Rider from Fate/Prototype) are bad guys who are chasing down protagonist Yashiro Isana (or Shiro for short) because they think that he's evil king. The whole thing about kings so far wasn't explained but might be revealed later. Going back to Shiro (which means white in Japanese), I don't like him much. On the other hand I'm very interested in Neko. She's been at center of all posters and other photos but has yet to make proper appearance. She was present in her cat form during this whole episode which makes me even curious about what kind of connection she has with Shiro. Also, Neko appeared once in her human form during this episode but nobody could see her except robot. o.O And then there's another important character - Kuro Yatogami (kuro means dark/back in Japanese). He saves Shiro from HOMRA gang only to reveal that he's been sent to kill evil king (in other words - Shiro).
But there many good things as well. Most notable ones are art & animation. The opening looks really awesome as well! Insane amount of budget must have went into animating this episode. I hope they won't run short on money later in the series.
I will give this anime two more episodes but if I won't be able to watch everything I want due to lack of time, K will be sacrificed in favor of other anime.