Problem A
Another Ancient Cipher
You have probably heard about the Caesar cipher: It is one of the most well-known ciphers out there. In an alternative timeline, the Roman emperor Caesar Augustus builds upon this cipher to create an encryption even harder to break: The Augustus cipher.
In the Caesar cipher, you shift each letter by a certain number of digits forwards or backwards, and start over at the other side if you roll over. For the English alphabet, the formulas for encrypting and decrypting the Caesar cipher are
\begin{align*} E_{Caesar}(M_ i, n) & = (M_ i + n) \mod 26 \\ D_{Caesar}(C_ i, n) & = (C_ i - n) \mod 26 \end{align*}Where $M_ i$ and $C_ i$ is the ordinal number of $i$th letter in the message and the ciphertext, respectively, and the number $n$ is the integer to shift by. (The ordinal number of a letter is defined as $\texttt{a} \to 0, \texttt{b} \to 1, \ldots , \texttt{z} \to 25$ for the Latin alphabet.)
The Augustus cipher goes above and beyond, and uses a key to encrypt messages. The $i$th letter of the message is defined as
\[ E_{Augustus}(M_ i, K_ i) = \begin{cases} E_{Caesar}(M_ i, K_ i) & \quad \text {if } M_ i \text { is even}\\ E_{Caesar}(M_ i, -K_ i) & \quad \text {if } M_ i \text { is odd} \end{cases} \]If there are more letters in the message than in the key, the key is repeated. For example, the $4$th $0$-indexed letter of the key key is k, the $5$th is e and so on.
Adam has decided to use this cipher for his new social media platform CyberLounge, and has implemented code to encrypt the messages with the Augustus cipher. But Adam hasn’t yet found a way to decrypt the messages! Could you help him with the decryption algorithm?
Input
The input consists of two lines. The first line contains the encrypted string $C$, and the second line contains the key $K$. Both strings contain only lowercase characters from the Latin alphabet (a-z).
Output
Output the decrypted message.
Limits
-
$0 < |C|, |K| \leq 200$
| Sample Input 1 | Sample Output 1 |
|---|---|
ccvpvygcoyjc cryptography |
attackatonce |
| Sample Input 2 | Sample Output 2 |
|---|---|
tnkkmbwctzhdjesfqugjmgcyzlpxeeyclhg augustusisthebest |
thequickbrownfoxjumpsoverthelazydog |
| Sample Input 3 | Sample Output 3 |
|---|---|
unnmzaxunlzjdzfnnejdx z |
toolazytomakeagoodkey |
