Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

If the function $f(x) = \begin{cases} \frac{2}{x} \left\{ \sin (k_1 + 1) x + \sin (k_2 - 1) x \right\}, & x < 0 \\ 4, & x = 0 \\ \frac{2}{x} \log_e \left( \frac{2 + k_1 x}{2 + k_2 x} \right), & x > 0 \end{cases}$ is continuous at $x = 0$, then $k_1^2 + k_2^2$ is