Suppose that we have an array A (ao, 21, 22, ..., An1] of integers and an array S = (S0, S1, ..., Sn-1) of partial sums of A, i.e., each element s; = Ci_oa; of S is the sum of the first j +1 elements of A. For example, we could have that A = [2,3, -4,2,1,6,-8,5, -12,4) and S = (2,5,1,3,4,10,2,7,-5, -1). Give a fast algorithm which, provided that the sum of the elements of A is odd, finds an odd element of A. Show that your algorithm is correct and analyze its running time by proving an explicit Big-O bound as a function of n. A solution that runs in N(n) time will receive no credit, as this is trivially achieved by checking elements one-by-one