Etched Emerald Orbs

An archaeologist team found a tomb of the ancient tribe and discovered $2^{125}$ emerald orbs inside the tomb. The ancient tribe etched a number on each emerald orb. The archaeologists spent two decades realizing that each emerald orb has a unique number. The numbers run from $1$ to $2^{125}$, written in the ancient language.

Eddy, the only mathematician on the archaeologist team, recently figured out the relation between the number $k$ and the emerald orb numbered $k$. The weight of the emerald orb numbered $k$ is exactly $\frac{1}{k}$ grams. Since every orb has a distinct number, no two orbs have the same weight.

Eddy proposes a hypothesis: the ancient tribe used these orbs to represent weights less than $1$ gram. Clearly the orb numbered $k$ represents $\frac{1}{k}$ gram. Eddy then tries to represent $\frac{2}{k}$ grams for $3 \le k \le 4 \times 10^{18}$ with two orbs. He finds that the orbs numbered $2$ and $6$ represent $\frac{2}{3} = \frac{1}{2} + \frac{1}{6}$ grams. Similarly, the orbs numbered $3$ and $15$ represent $\frac{2}{5} = \frac{1}{3} + \frac{1}{15}$ grams.

Write a program that checks whether two orbs can represent $\frac{2}{k}$ grams for a given integer $k$. If several pairs of orbs represent $\frac{2}{k}$ grams, output the pair that minimizes the sum of the numbers on them. If no pair exists, output $-1$.

The input contains one positive integer $k$.

If there is no solution, output $-1$. Otherwise, output two distinct integers $x$ and $y$ separated by a space, where $\frac{2}{k} = \frac{1}{x} + \frac{1}{y}$ and $1 \le x < y \le 2^{125}$. If there are multiple solutions, output the one that minimizes $x + y$.

$3 \le k \le 4 \times 10^{18}$.