We are running programs on a machine with the following characteristics:

Values of type int are $32$ bits. They are represented in two$$s complement, and they are right

shifted arithmetically. Values of type unsigned are $32$ bits and are right shifted logically$.$

We generate arbitrary values x$,$ y$,$ and u as follows. $($Assume that random$\_$int can return any int

value, and random$\_$unsigned can return any unsigned value.