2017 InIMC keystage3-IWYMIC team Question 8

Suppose $x,y$ and $z$ are all non-negative real numbers. Let $k$ and $m$ be the minimum possible values of $\frac{x^2+y^2+z^2+1}{xy+yz+z}$ and $\frac{x^2+y^2+z^2+1}{xy+y+z}$ respectively. Find $km+k+m$.