Question $3$Regular languages closed under operations

Let $\backslash$Sigma be some alphabet. For a natural number k$,$ we define the following operation on

the set of all languages over $\backslash$Sigma $.$ The operation MOVE$$k$($L$1,$ L$2)$ takes in two languages

L$1$ and L$2$ and outputs the language L$2$ where the set of words of length k from L$2$

have been replaces with the set of words from L$1$ with length k:

MOVE$$k$($L$1,$ L$2)=\{$w in $\backslash$Sigma

$$

$||$w$|=$ k and w in L$1,$ or $|$w$|=$ k and w in L$2\},$

where $\backslash$Sigma $$

is the set of all words over $\backslash$Sigma $.$

Prove that, for any k in N the class of regular languages is closed under the operation

MOVE$$k$.$