Implement a Polynomial class to represent polynomial expressions. A polynomial expression may have any number of terms. Class methods should support the standard operations such as addition, subtraction, multiplication, and division. The user should be able to create arbitrary polynomial expressions such as

where a**b means a^b. Also, there should be a method that allows the user to encode a polynomial as a bit-string. For example, the bit-string

1101

represents the polynomial expression

because the bit-string contains a 1 in positions 0, 2, and 3.