Please someone tell me that he and his baby will survive

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Yes, they both will survive. And the child will look like Ijun before he took Jaekyung's body.

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Then the child is Injun's and not from Jaekyung's body?

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Yup! Injun's parents will think their elder son had the baby with Uke. But then the misunderstanding will be cleared and his parents will also know that their younger son is alive in Jaekyung's body.