Asterisk Killer Sudoku

The objective is to fill the grid with numbers from 1 to 9 in a way that the following conditions are met: Each row, column, and nonet contains each number exactly once. The sum of all numbers in a cage must match the small number printed in its corner. No number appears more than once in a cage. (This is the standard rule for killer sudokus, and implies that no cage can include more than 9 cells.) In Asterisk Sudoku there is an additional area, shown on the grid by shading nine specially selected cells. Those nine cells must also contain 1 to 9