Question 8: Consider the following recursive algorithm, which takes as input a sequence (, , . . . , an) of n numbers, where n is a power of two, i.e., n-2k for some integer k > 0: Algorithm MYSTERY(al, a2, , an): if n 1 then return ai else for i 1 to n/2 endfor MYSTERY(bi, b2,... ,bn/2 endif Determine the output of algorithm MYSTERY(a1, a2, , an). As always. Justify your answer. . For any integer n 2 1 that is a power of two, let (n) be the number of times that line (*) is executed when running algorithm MYSTERY(a1, a2 . , an). Derive a recurrence for T(n) and use it to prove that for any integer n 2 1 that is a power of two, T(n)-n-1