DES has a somewhat surprising property related to bitwise complement of its input and output. We will investigate the property in this problem. We denote the bitwise complement of a number A (that is, all bits are flipped) by A. We want to show that

if y = DES_k (x) then y = DES_k (x). This states that if we complement the plaintext and the key, then the ciphertext output will also be the complement of the original ciphertext. Your task is to prove this property.