Which question tag should follow *He must have overslept* ?

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> *He must have overslept, **mustn't he** ?*
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or

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> *He must have overslept, **hasn't he** ?*
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or even

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> *He must have overslept, **didn't he** ?*
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What motivates my question is that adding *not* to modal *must* usually changes its meaning from the logical deduction that something is/was the case to prohibition, doesn't it?