OCaml combine fprintf and sprintf

I want to write a function that can either print something to a string or to an out_channel. I'm stuck with the internal format stuff however.

My approach is something like this:

type pr_target = Channel of out_channel | StrRef of string reflet my_print target fmt = match target with  | Channel ch -> fprintf ch fmt  | StrRef str -> str := !str ^ sprintf fmt

This gives a type errors as the two uses of fmt are different: fprintf takes an ('a, out_channel, unit) format while sprintf takes an ('a, unit, string) format.

How can I write such a function? I'm not super proficient with modules or OCamls polymorphism.