Let \( f:\mathbb{R}-\{0\}\rightarrow(-\infty,1) \) be a polynomial of degree \( 2 \), satisfying \(\displaystyle f(x)f\!\left(\frac{1}{x}\right)=f(x)+f\!\left(\frac{1}{x}\right) \). If \( f(k)=-2k \), then the sum of squares of all possible values of \( k \) is:
