\textbf{119.} If $\displaystyle\lim_{x \to -\infty} \frac{\sqrt[5\circ]{(a^2x^2-1)(a^4x^4-1)\cdots(a^{100}x^{100}-1)}}{a^{49}x^k - 1} = -1$, what are the values of $a$ and $k$?
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(1) $k = 51,\ a = -1$ \hfill (2) $k = 51,\ a = 1$
(3) $k = 49,\ a = -1$ \hfill (4) $k = 49,\ a = 1$
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