In Java, Please provide a detailed and step by step on the code, Thank you!

Problem Description:

A school has $100$ lockers and $100$ students. All lockers are closed on the first day of school. As the students enter, the first student, denoted S$1,$ opens every locker. Then the second student, S$2,$ begins with the second locker, denoted L$2,$ and closes every other locker. Student S$3$ begins with the third locker and changes every third locker $($closes it if it was open, and opens it if it was closed$).$ Student S$4$ begins with locker L$4$ and changes every fourth locker. Student S$5$ starts with L$5$ and changes every fifth locker, and so on$,$ until student S$100$ changes L$100.$

After all the students have passed through the building and changed the lockers, which lockers are open? Write a program to find your answer. The program should display the answer like this:

Locker x is open

Locker y is open

$...$

Locker z is open

$($Hint: Use an array of $100$ boolean elements, each of which indicates whether a locker is open $($true$)$ or closed $($false$).$ Initially, all lockers are closed.$)$