A Turing machine with double infinite tape is like an ordinary Turing machine, but its tape is infinite in both directions, to the left and to the right. Prove that Turing machine with double infinite tape is equivalent to the ordinary Turing machine. (Note: you can assume that the tape is initially filled with blanks except for the portion that contains the input. Computation is defined as usual except that the head never encounters an end to the tape as it moves leftward. Show that this type of Turing machine recognizes the class of Turing-recognizable languages.