Question 8: Consider the following recursive algorithm, which takes as input a sequence (a!, , . . . , an) Of n numbers, where n is a power of two, i.e., n-2k for some integer k 0 Algorithm MYSTERY(a1, a2, , an): ifn=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 T(n) be the number of times that line (*) is executed when running algorithm MYSTERY(al, a2 ,an). Derive a recurrence for T(n) and use it to prove that for any integer n 1 that is a power of two, T(n) = n-1