relation between ntime and dtime Given DTIME($n^2$) contains NTIME($n^{100}$) show that P=NP.

I think it's supposed to be straightforward but I just can't see it.

Take $L$, a language in NP. $L$ has a Turing machine which runs in NTIME$(f(n))$. If $f(n)$ is $\Omega(n^{100})$ it's obvious, but what about $O(n^{100})$?
Hint: What is the time complexity of the fastest nondeterministic Turing machine that is a decider for $SAT$?