Is it normal that i want to kill my bullies?

When I was younger, I was always a loner. A weirdo. A freak. No matter how much I tried to make friends, they left me out and excluded me, and I felt really isolated. It was bad enough being left out and made to feel like a weirdo, but some even bullied me. They called me names, tripped me up etc. But nothing too serious.
Until one day, I was walking home from school, when a whole gang of my peers came up surrounding me. There must have been at least 7 of them. They circled me, telling me I was crazy and nobody liked me, and then beat me up really badly. They left me there in the dirt, wounded and the pain was too much to bear, mentally and physically. I had to move to a new town and everything because they had made my life hell. I've never been the same since.
From that day, I've sworn to get revenge on them, for what they did to me. I remember each of their names and faces well. I've been planning this for a while now. My plan is to hunt down each of them and kill them, one by one. It's what they deserve. The filth that they are. They are the scum of the Earth and need to be eliminated from this world.
This isn't just a fantasy I've had, I've literally got the murder plans for those bullies, how I'm going to carry out and dispose of each one, without leaving a trace. I want to go through with it and make them feel the pain that they caused me to feel. I believe that it's right and it's what is needed. I may be twisted and maybe even a little insane, but I know I'm not evil. They hurt me, but they could hurt other people and should be stopped. Someone's got to do it. Someone's got to dispose of the filth from this world. Is it normal to actively plan to murder the people who have bullied you? Not that it matters anyway, for I'll always be a "freak."