Re-staking rewards question?

I see that rewards are automatically added to your wallet but are they automatically re-delegated according to your set choice?

For example, you delegate 10k ADA to stakepool X. You get a 20 ADA reward. Are you now staking 10,020 ADA to stakepool X or are there 20 ADA just sitting in your wallet doing nothing?

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They are automatically delegated to