Google Sheets – Assign Value to Cell Based on Another Cell’s List

Here is the situation: I have column I with the header as "Design" and column J with the header as "DETAIL", then I have column K with a header as "TYPE_W". OK on this last column K, I selected from cell K2 up to K22 and added a data validation Criteria: LIST OF ITEMS then DETAIL,DESIGN,OTHER, so what I want to accomplish is:

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