Calendar Date Picker with calculations bettween two dates

We currently have an standard reservation form you have to pick a day, month, year and the number of nights you want. We would like a date picker calendar that fills day, month and year options in the form and then based on the number of nights you choose, it should show you the check-out date. We're attaching a graphic on how should it work and would also provide current form to be modified. Preferebly based in jquery.