Instant
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If a spell with 
in its mana cost is countered this way, is the value chosen as the spell was cast.
This can be used to cast either face of a modal double-faced card, but only if the face you are casting has an equal or lesser mana value than the target spell.
If you target a spell that can’t be countered, like Heated Debate, you won’t counter the spell, but you will get to cast a spell with an equal or lesser mana value.
If you cast a spell “without paying its mana cost,” you can’t pay any alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, you must pay those.
If the spell you cast has in its mana cost, you must choose 0 as the value of X.