Select unique combinations (unique on both sides) - sql

Question

EDIT: added a link to Fiddle for a more comprehensive sample (actual dataset)
I wonder if the below is possible in SQL, in BigQuery in particular, and in one SELECT statement.
Consider following input:
Key | Value
-----|-------
a | 2
a | 3
b | 2
b | 3
b | 5
c | 2
c | 5
c | 7
Logic: select the lowest value "available" for each key. Available meaning not yet assigned/used. See below.
Key | Value | Rule
-----|-------|--------------------------------------------
a | 2 | keep
a | 3 | ignore because key "a" has a value already
b | 2 | ignore because value "2" was already used
b | 3 | keep
b | 5 | ignore because key "b" has a value already
c | 2 | ignore because value "2" was already used
c | 5 | keep
c | 7 | ignore because key "c" has a value already
Hence expected outcome:
Key | Value
-----|-------
a | 2
b | 3
c | 5
Here the SQL to create the dummy table:
with t as ( select
'a' key, 2 value UNION ALL select 'a', 3
UNION ALL select 'b', 2 UNION ALL select 'b', 3 UNION ALL select 'b', 5
UNION ALL select 'c', 2 UNION ALL select 'c', 5 UNION ALL select 'c', 7
)
select * from t
EDIT: here another dataset
Not sure what combination of FULL JOIN, DISTINCT, ARRAY or WINDOW functions I can use.
Any guidance is appreciated.

Answer 1

EDIT: This is an incorrect answer that worked with the original example dataset, but has issues (as seen with comprehensive sample). I'm leaving it here for now to maintain comment history.
I don't have a specific BigQuery answer, but here is one SQL solution using a Common Table Expression and recursion.
WITH MyCTE AS
(
/* ANCHOR SUBQUERY */
SELECT MyKey, MyValue
FROM MyTable t
WHERE t.MyKey = (SELECT MIN(MyKey) FROM MyTable)
UNION ALL
/* RECURSIVE SUBQUERY */
SELECT t.MyKey, t.MyValue
FROM MyTable t
INNER JOIN MyCTE c
ON c.MyKey < t.MyKey
AND c.MyValue < t.MyValue
)
SELECT MyKey, MIN(MyValue)
FROM MyCTE
GROUP BY MyKey
;
Results:
Key | Value
-----|-------
a | 2
b | 3
c | 5
SQL Fiddle