Josephus attended a party where they had a rather strange raffle. Everyone was to stand in a circle, and every Mth person was to be eliminated until only one person was remaining, who won the lawnmower. Write the function Josephus, which takes as parameters a vector representing the N guests at the party in the order they line up for the raffle, and the integer M, giving which person will be eliminated at each turn. Your function should return a string giving the name of the winner of the raffle (the last person standing). Hint: While there is a mathematical solution, a queue will be much more straightforward.

File account.java (see previous exercise) contains a definition for a simple bank account class with methods to withdraw, deposit, get the balance and account number, and return a string representation. note that the constructor for this class creates a random account number. save this class to your directory and study it to see how it works. then write the following additional code: 1. suppose the bank wants to keep track of how many accounts exist. a. declare a private static integer variable numaccounts to hold this value. like all instance and static variables, it will be initialized (to 0, since it’s an int) automatically. b. add code to the constructor to increment this variable every time an account is created. c. add a static method getnumaccounts that returns the total number of accounts. think about why this method should be static - its information is not related to any particular account. d. file testaccounts1.java contains a simple program that creates the specified number of bank accounts then uses the getnumaccounts method to find how many accounts were created. save it to your directory, then use it to test your modified account class.