There is even an oracle in which BPP=EXPNP (and hence P<NP<BPP=EXP=NEXP), which can be iteratively constructed as follows. For a fixed ENP (relativized) complete problem, the oracle will give correct answers with high probability if queried with the problem instance followed by a random string of length "kn" ("n" is instance length; "k" is an appropriate small constant). Start with "n"=1. For every instance of the problem of length "n" fix oracle answers (see lemma below) to fix the instance output. Next, provide the instance outputs for queries consisting of the instance followed by "kn"-length string, and then treat output for queries of length ≤("k"+1)"n" as fixed, and proceed with instances of length "n"+1.