$--$show all steps$---$: Consider a modified Vigen$$re cipher where the set of characters are the English alphabet plus the numbers from $0$ to $9.$

$($i$)$ If Pi is the ith digit of the plaintext, Ci is the ith digit of the ciphertext, and Ki is the ith digit of the key, write equations for the encryption and decryption operations.

$($ii$)($ii$)$ For P $=$ BN$3$LS$68$MSZ$9$WE$2$ and keyword $=$ J$7$K$5$R$,$ what is C$?$