Is there an easy way to find multiple header columns given a set of data?

Question

I have a sheet that looks like this:

I'd like to have a formula that queries the data in A2:E7 and pulls the corresponding column headers from A1:E1. The trick is that values may appear more than once.

Sample results would look like this:

Example sheet: https://docs.google.com/spreadsheets/d/1Zr_q8nwYPixUjxWYdT-WlQLiGIUzqoK_cSQXSp19nJg

Answer 1

use:

=ARRAYFORMULA(IFERROR(TRIM(SPLIT(IFNA(VLOOKUP(G1:G, 
 SPLIT(FLATTEN(QUERY(TRANSPOSE(QUERY(QUERY(UNIQUE(SPLIT(FLATTEN(
 IF(A2:E="",,A2:E&"♂×"&A1:E1&"♀×"&A1:E1)), "×")), 
 "select Col1,max(Col2) 
  where Col2 is not null 
  group by Col1
  pivot Col3"), 
 "offset 1", 0)),,9^9)), "♂"), 2, 0)), "♀"))))

---

update:

=ARRAYFORMULA(ARRAY_CONSTRAIN(IFERROR(TRIM(SPLIT(IFNA(VLOOKUP(G1:G, 
 SPLIT(FLATTEN(QUERY(TRANSPOSE(QUERY(QUERY(UNIQUE(SPLIT(FLATTEN(
 IF(A2:E="",,A2:E&"♂×"&A1:E1&"♀×"&A1:E1)), "×")), 
 "select Col1,max(Col2) 
  where Col2 is not null 
  group by Col1
  pivot Col3"), 
 "offset 1", 0)),,9^9)), "♂"), 2, 0)), "♀"))), 9^9, 2))