Suppose there is a credit store in your city that allows you to go for up to three purchases on credit. But at the time of third purchase, you have to pay for the highest bill out of the three purchases. Write a program using Stack class in Java to demonstrate the following activities:

1. Create an empty stack named "bills".

2. Push the bill amounts of three purchases into the stack.

3. Pop the three bills out of the stack and put them in different variables.

4. Display the highest bill for payment.

5. Push the remaining two bills back into the stack.

6. Display the stack before and after the payment.