CMO 1991 Problem 2

Given $I=[0,1]$ and $G=\{(x,y)|x,y \in I\}$ , find all functions $f:G\rightarrow I$ , such that $\forall x,y,z \in I$ we have: i. $f(f(x,y),z)=f(x,f(y,z))$ ; ii. $f(x,1)=x, f(1,y)=y$ ; iii. $f(zx,zy)=z^kf(x,y)$ . ( $k$ is a positive real number irrelevant to $x,y,z$ .)