# compact Riemann surface and branched cover

Show that a compact Riemann surface admits a branched cover of the sphere with only simple branch points.

I have this problem and it seems to me that the way is to use Riemann Roch theorem, but I do not know how to exactly apply!

Any help is welcome.

Choose a branch set $$D$$ of size greater than or equal to the genus. Then by Riemann-Roch, the dimension of the space of meromorphic functions branching on $$D$$ with at worst simple poles is greater than or equal to $$1$$.