Oh thanks very much guys. try_files worked well. I tried using try_files before, but mistakenly wrote it as something like this

try_files dump/$1-s.jpg dump/$1-s.png 404;

The correct working line should be like this

try_files /dump/$1-s.jpg /dump/$1-s.png =404;

And I didn't expect IF is evil. Suprise!

Thanks again.