If $\alpha, \beta \neq 0$, and $f(n) = \alpha^n+\beta^n$ and $\begin{vmatrix} 3 & 1+f(1) & 1+f(2)\\ 1+f(1)& 1+f(2) &1+f(3) \\ 1+f(2)&1+f(3) & 1+f(4) \end{vmatrix}$$=K(1-\alpha)^2\;(1-\beta)^2\;(\alpha-\beta)^2$, then $K$ is equal to

Question

$\begin{array}{1 1} \alpha \beta \\ \frac{\alpha}{\beta} \\ 1 \\ -1 \end{array}$