Consider the following program, where a and n are positive integers. Input: a, n x = a; m = n; y while (m > 1) { if m is even } X = X*X; m = m/2; if m is odd y x*y; X = X*X; m = Output x*y = 1; = (m-1)/2; Show by induction that the above loop has the following invariant: a = xm x y. What does the above program compute?