## SUBJECT I

If the natural number $x$ satisfies the equation $\left\lfloor(4026: 61: 33-x): 2013^{0}+3\right\rfloor \cdot 6-24=0$ and $y=\left(2+2^{2}+\ldots+2^{2013}\right):\left(4^{1007}-2\right) \cdot 2013$, find $x^{y}$ and $y^{x}$.
## SUBJECT I

| $x=1$ | $\mathbf{3 p}$ |
| :--- | :--- |
| $y=2013$ | $\mathbf{3 p}$ |
| $x^{y}=1, y^{x}=2013$ | $\mathbf{1 p}$ |