Use a Finite State Machine (FSM) to solve the following problem: A sequence detector receives as its inputs the integers 1, 5, and 10 in an arbitrary order, one integer at a time. Once the total sum of the received numbers exceeds the value 30, the FSM outputs the integer value 1. Moreover, the difference between the total sum of the received inputs and 30 must be covered using the smallest number of integer values 1 and 5. The FSM must display the smallest number of the values that cover the difference between the total sum and 30.