Program 1: Given a date, calculate the day of the week on which it falls. We will write a program that given any valid date since January 1, 1900, will then display the day of the week on which the date fell. (You may assume that the user will input a valid date) Your main method will prompt the user for a date in the format MMDD/YYYY It will read the date as a string, and then extract the day, month, and year from the String (using methods from class string) and convert them to integers (using methods from class Integer). Using the algorithm given below, you program should calculate the day of the week, and then print it out. IE: For the date 1019/2015 your program should display a message in the format: Monday, October 19,2015 NOTE: date. Each execution of the program will process a single Note, all variables are integers and the divisions are integer divisions. y= year-a m month + 12 x a-2 The month, day, and year variables used in the equation are the integer date values (10, 19 and 2015) from the previous example). The final value of daynum is 0-6 with 0 representing Sunday, and 6 representing Saturday. To determine the correct day name and month name, you will need to use a switch/case statement, which is explained in your text in chapter 5. A sample is given below A partially completed switch statement for the month name is given below String monthName; /declare this variable switch( month) case 1: monthName "January" break; case 2: monthName "February" break; otherwise: The month, day, and year variables used in the equation are the integer date values (10, 19 and 2015) from the previous example). The final value of daynum is 0-6 with 0 representing Sunday, and 6 representing Saturday. To determine the correct day name and month name, you will need to use a switch/case statement, which is explained in your text in chapter 5. A sample is given below A partially completed switch statement for the month name is given below: String monthName; I/declare this variable switch( month) case 1: monthName "January" break; case 2 monthName "February"; break: otherwise month Name- "Invalid Month!! A partially completed switch statement for the name of the day of the week is: String dayName switch( dayNum) case 0: dayName "Sunday" break; case 1: dayNameMonday" break; otherwise day-Name ="Invalid DAY. What to submit: Your application program in the form of a .java file