Alice has a cipher machine whose encryption steps are as follows:

1. Let the message m be represented as a natural number m=abcde... ;
2. Add the digits in m to obtain Sm=a+b+c+d+e+ ;
3. Then invert the order of the digits in m to obtain m=...edcba ;
4. The ciphertext c is given as c=m+2Sm .

Unfortunately due to a hardware error the cipher machine behaves erratically: sometimes it works correctly, sometimes it outputs a random number.

After encryption of her secret number $m$, Alice found out that the result c=2k for some kZ . Is the ciphertext c obtained by Alice a genuine encryption or a random output? Justify