Let $X$ be a normal variety and $f:Y\rightarrow X$ a birational morphism, contracting exceptional divisors $E_1,\dots,E_k$ onto the singular locus of $X$, with $Y$ smooth.

In this situation is $Pic(Y)$ generated by $f^{*}Pic(X)$ and the exceptional divisors $E_1,\dots,E_k$?