A TM with an oracle for language L is a TM that has a magical zero-time call to L; by this, we mean that the TM can present an input x to the oracle, and the oracle will return, in zero time, whether or not x ? L. (There is time needed in presenting the input to the oracle, however). If the TM is M, we call this oracle-equipped TM M^L. For a language B, call P^B to be the set of all languages that are polynomial-time solvable with an oracle for language B. If B = P, then this means that the oracles language can be any desired language in P.

Show that P^P = P. (i.e. P is low for itself.)