Let K $=111...111$ be the DES key consisting of all $1$s$.$ Show that if EK$($P$)=$ C$,$ then EK$($C$)=$

P$,$ so encryption twice with this key returns the plaintext. $($Hint: The round keys are

sampled from K$.$ Decryption uses these keys in reverse order.$)$

$($b$)$ Find another key with the same property as K in part $($a$).$