I'm trying to solve https://cses.fi/problemset/task/2183, and I'm completely baffled since every approach I come up with looks to violate the subset sum problem being NP complete for finding a specific subset that sums to N. I'd appreciate a nudge in the right direction.

My observations so far:

• If $$$1,2,4,...,2^i$$$ are in $$$X$$$, then $$$MEX \gt = 2^{i+1}$$$

• $$$MEX \lt = 1 + (x_1 + \ldots + x_n)$$$

• $$$MEX = 1$$$ if $$$\min(X) \gt 1$$$

None of these observations seem sufficient in general.