APMO 2011 Problem 5

Determine all functions $f:\mathbb{R}\to\mathbb{R}$ , where $\mathbb{R}$ is the set of all real numbers, satisfying the following two conditions:

1. There exists a real number $M$ such that for every real number $x,f(x)<M$ is satisfied.
2. For every pair of real numbers $x$ and $y$ , $$f(xf(y))+yf(x)=xf(y)+f(xy)$$ is satisfied.