A Random-Access Turing machine (RA-TM) is similar to the standard, single-tape, deter- ministic TM except for its transition function. On a transition, a RA-TM can move its head a finite, but arbitrary distance from its current location. Formally, the transition function is:

? : Q ? ? Q ? ({L, R} N)

For example, ?(qi, b) = (qj , c, (L, n)) will cause the RA-TMs head to move n places to the left (stopping at the left-most cell if the jump would cause the head to move off the tape). Prove that every RA-TM has an equivalent standard, single-tape, deterministic TM.