Is $MIN_{TM}$ not in $\overline{RE\cup coRE}$


Given the language:

$ MIN_{TM}$ = $ \{ \langle M,k\rangle: there\ exists\ a\ TM\ D\ s.t.\ L(M)=L(D)\ and\ D\ has\ less\ than\ k\ states \}$

I need to prove if this language is in $ R$ or $ RE-R$ or $ coRE-R$ or $ \overline{RE\cup coRE}$ .

I suspect this language is in $ \overline{RE\cup coRE}$ but I can’t prove it. (I Tried using reduction but no help).