[SQL] Use multiple conflict_target in ON CONFLICT clause

I have two separately unique columns in a table: col1, col2. Both have a unique index (col1 is unique and so is col2).

I need INSERT ... ON CONFLICT ... DO UPDATE syntax, and update other columns in case of a conflict, but I can't use both columns as conflict_target.

It works:

INSERT INTO table
...
ON CONFLICT ( col1 )
DO UPDATE
SET
-- update needed columns here


But how to do this for several columns, something like this:

...
ON CONFLICT ( col1, col2 )
DO UPDATE
SET
....


Currently using Postgres 9.5.

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