Divisible by this year??? (Part 11: The Last Stand)

Let's make the end of 2014 very memorable.

I have a dartboard which has the shape identical to the intersection of $y\quad =\quad x^x +{ x }^{ \left\lfloor x \right\rfloor }+{ \left\lfloor x \right\rfloor }^{ x }+{\left\lfloor x \right\rfloor }^{ \left\lfloor x \right\rfloor }$ , $x - 1 = 0$ , $x - 5 = 0$ , and $y = 0$

Its bull's-eye, located at the center of the dartboard, has the shape identical to the intersection of $y\quad=\quad x +\left| x \right| + x\left| x \right|$ , $x + 7 = 0$ , $x - 7 = 0$ , and $y = 0$

Me and my friend, Devonna, made a bet. If I hit the bull's-eye 2 OR 5 times, I will win. Otherwise, she will win. We will do this while wearing blindfolds.

Given that we have 5 darts each, and also assuming that all of the darts hit the dartboard, let $p$ be the probability that I will win or in other words, the probability that I hit the bull's-eye 2 OR 5 times.

Also let $A$ be the value of $\left\lfloor 10000p \right\rfloor$ .

Then find the smallest positive integer $n$ such that ${ A }^{ n } - B \equiv 0(mod \quad 2014)$ where $B$ is a perfect square less than $2014$ .