Minato is bemused by the hug but not at all embarrassed. He oftentimes doesn't know what to do with physical contact, but it doesn't bother him either. He's neutral towards it, and if it's a neutrality he's learned from lack of exposure, he doesn't dwell on it. Minato isn't someone who craves things that he doesn't have.

He appreciates what he has now instead, belatedly raising his arms to return it and shortly thereafter having to lower them again. He keeps his left loosely curled around Ken's shoulders, not contesting it as he hides his face in his jacket.

"You're welcome."

It's now, at last, that Minato feels the tension in his chest ease, that wondering that was constricting it, and his breath comes easily again.

Ken is going to be alright. He'll make sure of it.