I have problems with permissions using xargs with rm

I have remove.txt file containing a.txt and b.txt as text. All files are in the same folder, I set chmod 777 for all those files. Now, when I run sudo cat remove.txt | xargs rm I get Permission denied for deletion of those two files listed in remove.txt. What am I doing wrong? I guess question now would be where to put sudo?


sudo cat remove.txt |  xargs sudo rm