Conditional formatting between columns

I have column I the last time the patient was seen. Column J as the date when a quarterly payment is due from a patient’s insurance. Column K is the date the patient was most recently seen.

With this particular insurance, we can only bill every 90 days and the patient has to have had to been actually seen sometime within 90 days from the LAST time they were in.

So what I want:
If in column I, I put 3/1/2022 as the last time they were in.

Column J I would put 6/1/22 because that’s technically the soonest we COULD bill.

I am going to type in Column K when the patient was seen and it would be a date between 3/1/22 and 6/1/22. I would like if I type in column K a date that is eligible, such as 4/15/22, column K to turn green, using conditional formatting. But I don’t want data that ISN’T eligible to turn green, like if I type 1/1/22, since it is not in between 3/1 and 6/1. I thought the "IF" formulas would be a good place to start but can't figure it out.

So IF the date I enter in column K is in between the dates listed on columns I and J, then K column turns green.

Attached is the spreadsheet.

Much obliged!