b) A modular-adder device 'M' operates with 16-bit registers. You give it two 16-bit natural numbers 'a' and 'b'. It adds them, divides by 2^16, keeps the quotient 'q' a secret, and publishes the remainder 'r'. Hint: Before answering, experiment with small addition tables. i) If a = 23,979 and r = 63,400, what are 'b' and 'q'? ii) If a = 33,472 and r = 8,047, what are 'b' and