Kurepa trees and inaccessible cardinals in $L$

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Given a regular uncountable cardinal $\kappa$ we say that a $\kappa-$tree is $\kappa-$Kurepa if it has at least $\kappa^+$ branches. If $\kappa=\omega_1$ we simply say that $T$ is Kurepa. In this respect, my question is the following:

Why the non existence of Kurepa trees implies that $\omega_2$ is an inaccessible in Gödel universe $L$?

Is someone willing to give me a proof of this fact?

Thanks!