Find the value of $K$ for the unity$-$feedback system shown below, where $G(s)=\frac{K(s+3)}{s^2(s+7)}$ if the input is $10t^{2}u(t),$ and the desired steady$-$state error is $0\mathrm{.}061$ for this input.

$K=16\mathrm{.}4$

$K=164$

$K=210$

$K=325$