I have a new line conversion problem of a file from one format to another.

I used the follwing code to remove the ^M character:

perl -pe -e 's/rn|n|r/n/g' "inputfile"

and it succesfully removed the ^M character.
The problem is that I also need to concatenate the line after the ^M character to the end of the line where the ^M character appeared. I’ll explain it better with an example, suppose this is my line of the text file:
I am new^M
here

The code I wrote above converts it into:
I am new
here

but I need:
I am new here

Hope it was clear, thanks to anyone who’ll reply