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As long as any of its targets are legal at the time Comet Storm resolves, Comet Storm will deal X damage to each of those legal targets.
The number of targets you choose for Comet Storm is one more than the number of times it's kicked. First you declare how many times you're going to kick the spell (at the same time you declare the value of X), then you choose the targets accordingly, then you pay the costs. No player can respond between the time you declare how many times you'll kick the spell and the time you choose the targets.
Each target you choose must be different.
For example, if you want Comet Storm to deal 4 damage to each of three different targets, that means X is 4 and you're kicking the spell twice. You'll pay a mana cost of , plus a kicker cost of , plus another kicker cost of , for a total of .
The kicker ability doesn't let you pay a kicker cost more than once.
If you copy a kicked spell on the stack, the copy is also kicked. If the copied spell is a permanent spell, the token the copy of that spell becomes when it enters is also kicked.
If a card or token enters as a copy of a permanent, the new permanent isn't kicked, even if the original was.
If you put a permanent with a kicker ability onto the battlefield without casting it, you can't kick it.
If a spell's kicker cost was paid, the spell is "kicked."
To determine a spell's total cost, start with the mana cost (or an alternative cost if another card's effect allows you to pay one instead), add any cost increases (such as kicker), then apply any cost reductions. The spell's mana value remains unchanged, no matter what the total cost to cast it was.