This digital logic problem was solved at least partially incorrectly. How would it be solved correctly?

$(20$ points$)$ Design a counter such that if the variable C$=1$ it will count $310231023...$ If C$=0$ it will toggle the current count. Fill in the truth table below.

Use D FFs for the design and Implement the Next State Logic using appropriately sized MUXs. Draw the circuit diagram of the state machine.