Alice is using one$-$time pad and notices that when her key is the all$-$zeroes string k $=0,$ then Enc$($k$,$m$)=$ m and her message is sent in the clear! To avoid this problem, she decides to modify KeyGen to exclude the all$-$zeroes key. She modifies KeyGen to choose a key uniformly from $\{0,1\}\backslash \{0\},$ the set of all $-$bit strings except $0.$ In this way, she guarantees that her plaintext is never sent in the clear.Is it still true that the eavesdroppers ciphertext distribution is uniformly distributed on $\{0,1\}?$ Justify your answer.