Google sheets – Assign a value to the cell based on another list of cells of the item's value

Here is the situation: I have a column I with the heading as "Design" and column J with the heading as "DETAIL", then I have a column K with a header like "TYPE_W". OK in this last column K, I selected cell phone K2 until K22 and added a data validation criteria: LIST OF ARTICLES so DETAIL, DESIGN, OTHER, then what I want to achieve is:

If I select in K2 "DESIGN", I want on a cell phone I2 the value = Y, if DESIGN is not selected, then I want the value to be empty in I2, then the same for cell J2 if the value selected in K2 is "DETAIL", then I need to J2 A VALUE = Y otherwise I need an empty value, so of course I want this for all the cells below I Y J that a value in K If nothing is selected because nothing is imputed in that row, can anyone help?