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If you are instructed to cast a spell with overload "without paying its mana cost," you can't choose to pay its overload cost instead.

Because a spell with overload doesn't target when its overload cost is paid, it may affect permanents with hexproof or with protection from the appropriate color.

If you don't pay the overload cost of a spell with overload, that spell will have a single target. If you pay the overload cost, the spell won't have any targets.