I'm given a task to find (and prove) such language $L$ in the alphabet $\Sigma = \{a,b\}$ with all words less than $1000$ in length, for which any DFA/NFA will have more than $10^{10}$ of states. For the first part of the task, with DFA, I've found such language (see below), but can't think of solution for NFA. I even don't know if the same language can be the solution with NFA.
The language for DFA is $L = \{ ww : |w|=200 \}$.
Could you help me with this part of task, better not with actual solution, but with advice?
P.S.: it's my the very first homework on this topic.