Given an $X$ a Riemann surface, suppose $p_1, p_2, \dots, p_n$ are different points on $X$, and $r_1, r_2, \dots, r_n$ are integers. Is there a meromorphic function $f$ on $X$ such that each $p_i$ is a zero of $f$ and the order of $f$ on $p_i$ is $r_i$(i.e. $\operatorname{Ord}_f(p_i)=r_i$)?
Note that $X$ is not necessarily compact, so we can not use Riemann-Roch theorem.
Thanks in advance.