A modular-adder device 'M' operates with n-bit registers. You feed it two n-bit natural numbers 'a' and 'b'. It adds them, divides by 2^n, keeps the quotient 'q' a secret, and publishes the remainder 'r'. Hint: Before answering, experiment with small addition tables. i) If a = 2^(n-1) and r = 2^n - 1, what are 'b' and 'q'? ii) If a = 2^(n-1) and r = 2^(n-1) - 1, what are 'b' and 'q'?