Nested IFs formula to find matching values with multiple conditions

I'm trying to use a single Excel formula to perform a somewhat complex task.

I have 2 columns of numbers, sorted from highest to lowest. Probably 70% of the numbers match each other side-by-side, because both are sorted the same way.

The remainder do not match. I need a formula that will compare values in both columns, then do one of 3 things.

The worksheet appears like so:
(A) (B)
21 21
33 25
90 33
129 129
130 140
145 145

1. If the column A value matches the column B value, output "match"

2. If the column A value does not match the column B value, AND the column A value does not appear anywhere in column B, output "no match possible"

3. If the column A value does not match the column B value, AND the column A value appears somewhere in column B, output "match elsewhere"

I'm trying to do this using the IF statement and it's a miserable failure. Any ideas how I might tackle this?

I'm an Excel newbie :-(

Welcome to the forum.

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Place in C1:

=IF(A1=B1,"Match",IF(ISNA(MATCH(A1,B:B,0)),"No Match Possible","Match Elsewhere"))

Copy down to end of list.