Optional string with a required string in Regex

I need to detect class of strings which must include X, but may have Y optionally.

<<TAG##X#123>>
<<TAG##X#123##Y#456>>

So here’s the regex I tried, greps x but can’t detect y value:

(<<)(TAG##X#(?<x>.+)(##Y#(?<y>.+))?)(>>)

What am I missing?

>Solution :

(?<x>.+) matches the whole 123##Y#456 already.

Add a ? after the quantifier, to make this ungreedy: (?<x>.+?)

https://regex101.com/r/UuT50e/1